*CAMERON UNIVERSITY*

*DEPARTMENT OF MATHEMATICAL SCIENCES*

*LAWTON, OKLAHOMA
73505-6377, USA*

**CURRICULUM VITAE**

**IOANNIS KONSTANTINOS ARGYROS**

**1. PERSONAL**

NAME:
*Ioannis K. Argyros*

PLACE
OF BIRTH: *Athens, Greece*

CITIZENSHIP:
*USA*

ADDRESS:
*Cameron University, Department of Mathematical
Sciences, Lawton, OK 73505, USA*

E-MAIL: *iargyros@cameron.edu*

WEB PAGE: *http://www.cameron.edu/~ioannisa*

LIST OF MR AND CMP ITEMS: List of papers authored by Argyros, Ioannis, K.: http://www.ams.org/mrlookup

FAX: (580) 581-2616

TELEPHONE(S): (580) 581-2908 (office) or (580) 581-2481 (office of the secretary) or (580) 536-8754 (Home)

**2. STUDIES**

(1) 1983-1984 Ph.D. in Mathematics, University of Georgia, Athens, Georgia

(2) 1982-1983 M.Sc. in Mathematics, University of Georgia, Athens, Georgia

(3) 1974-1979 B.Sc. in Mathematics, University of Athens, Greece

**3. ACADEMIC EXPERIENCE**

(1) 1994-Present Full Professor, Cameron University, USA

(2) 1993-1994 Tenured Associate Professor, Cameron University, USA

(3) 1990-1993 Associate Professor, Cameron University, USA

(4) 1986-1990 Assistant Professor, New Mexico State University, USA

(5) 1984-1986 Visiting Assistant Professor, University of Iowa, USA

(6) 1982-1984 Teaching-Research Assistant, University of Georgia, USA

(7) 1979-1982 Serving the Greek Army, Greece

**4. SCIENTIFIC ACTIVITY**

__(A)
Fields of Interest/Research Has Been Conducted in:__

*(1) **Mathematical Analysis: *

(a) Functional analysis

(b) Operator theory. Worked on existence, uniqueness and solvability of Polynomial operator equations on a Banach space, Hilbert space and Riemannian manifolds

(c) Multilinear operator theory

(d) Fixed point theory

(e) Numerical functional analysis

(f) Numerical analysis

(g) Applied analysis

(h) Wavelets

(2)
Applied Mathematics/Analysis:

(a) Numerical solution of ordinary-partial differential-integral-functional equations on parallel computers

(b) Numerical methods

(c) Acceleration of convergence

(d) Numerical simulation; numerical approximation; interval arithmetic

(e) Numerical algebraic or transcendental equations

(f) Mathematical programming; optimization and variational techniques

(g) Computer arithmetic and numerical analysis; computer aspects of numerical algorithms

(h) Computer networks; discrete Mathematics in relation to computer science

(i) Theory of data

(j) Applications in mechanics, physics, chemistry, biology, technology and economics

(3)
Management Science

(4)
Wavelet and Neural Networks

(5) Mathematical
Economics (oligopoly theory, theory of games).

(6) Mathematical
Physics (elasticity, kinetic theory of gasses,
astrophysics, mechanics)

The American Mathematical Society subject classification codes for the above interests are: 12, 15, 26, 28, 34, 35, 39, 40, 45, 46, 47, 49, 65, 68, 85, 90.

Most problems in applied sciences can be brought in the form

*F*(*x*)
= 0,

where
*F* is an operator on some appropriate space. For example the above
equation may be a linear or a nonlinear system of equations on the *n*th
dimensional Euclidean space.

I derived such a system when I solved:

(a) A case of the Chandrasekhar's integral equation (Nobel Prize of Physics, 1983). This equation solves the problem of determination of the angular distribution of the radiant flux emerging from a plane radiation field;

(b) A problem from nonlinear elasticity theory, which pertains to the buckling of a thin shallow spherical shell clamped at the edge and under uniform external pressure;

(c) The problem of existence and uniqueness of equilibrium in oligopoly markets. Oligopoly is the state of industry where firms produce homogeneous goods (or close substitutes) and sell their products in a homogeneous market;

(d) Problems coordinating traffic at airports and highways;

(e) Problems involving the construction of safe bridges or buildings;

(f) Problems involving the location of moving objects like: missiles, airplanes, satellites, spaceships;

(g) Models describing the rate with which certain diseases (e.g. cancer) or infections spread on humans or animals;

(h) Models describing population growth or decay (e.g. bacteria on human skin or human population growth or decay). These models help us predict supplies needed for the preservation of human species;

(i) Models describing the behavior of economic markets (e.g. Wall Street Stock Market).

Note that the above is a very incomplete list of physical phenomena that can be brought in the form of the above equation. I just listed the areas where I have contributed with my research manuscripts, books and lectures.

Solutions of the above equation can be approximated by carefully designed numerical algorithms called Newton-like methods with the assistance of computers. Such numerical methods have been described in my published peer-reviewed manuscripts and books and lectures in computational Mathematics.

__(B) ____Editing__

1. I am the founder and Editor-in-Chief
of the *Southwest Journal of Pure and Applied Mathematics. * This is a peer-reviewed purely electronic journal established in 1995 at
Cameron University (1995-2004).
ISSN 1083-0464. Web Page: http://rattler.cameron.edu/swjpam/swjpam.html

*Serving at the editorial board:*

2. *Journal of Applied Mathematics and
Computing*
(1997-present). ISSN 1229-9502.

3. *Advances in Nonlinear Variational Inequalities** (ANVI) *(International Publications USA)
(1999-present). ISSN 1092-910X.

4. *Computational Analysis and
Applications* (Plenum
Publ.) (1998-2000). ISSN
1521-1398.

5. *International Journal of
Computational and Numerical Analysis and Applications*, ISSN 1311-6789 (2000-present),
(IJCNAA).

6. *International Journal of Pure and
Applied Mathematics*,
ISSN 1311-8080, (2001-present), (IJPAM).

7. *Mathematical Sciences Research
Journal*
(2002-present), ISSN 1537-5978.

8. International Review of Pure and
Applied Mathematics, (2004-present) Serial Publications

9. International Journal of Applied Mathematical
Sciences (2004-present) Global Publications, ISSN 09730176

10. Journal of Applied Functional
Analysis (2003-2005), Nova Science Corp.

11. International Journal of Theoretical
and Applied Mathematics (2005-Present), Serials Publications.

12. Communications on Applied Nonlinear Analysis, (2006-Present), International
Publications.

13. Advances in Nonlinear Analysis and
Applications (ANAA), (2006-Present),Serial Publications.

14. Mathematics Applied in Science and
Technology, (MAST), (2006-Present), http://www.ripublication.com/mast.htm

15. Antarctica Journal of Mathematics (2006-Present),
http://www.angelfire.com/0k3/prof/journa.html

16. Polimetrica,Polimetrica
Publisher,Corso Milano,Italy (2006-Present),Web Page: http://www.polimetrica.com

17. Punjab University Journal of Mathematics (2006-Present).

18. Mathematical
Reviews of the American Mathematical Society (August 2006-Present).

19. Journal of the Korean Society of Mathematics
Education Series B. Pure and Applied Mathematics (Associate Editor January
2007-Present). ISSN 1226-0657.

20. Arabian Journal of Mathematics and Mathematical Sciences (AJMMS) (November 2006-Present).

21. East Asian Journal of Mathematics, (Summer
2007-Present).

22. Advances and Applications in Mathematical
Sciences, July 27, 2008-Present.

23. International Journal of Mathematics and Computation, 2009-Present.

24. Communications of the Korean Mathematical
Society, Jan 1, 2010-Present.

25. Applied Mathematical and Computational Sciences, 11-9-2009-Present.

26. Applied Mathematics and Computation (Elsevier, Associate Editor) 1-2010-Present.

27. J. Mathematical and Computational
sciences, ISSN:1927-5307

28. Contemporary Mathematics and
statistics, uscip.org/journalsDetail.aspx?journalID=30

29. Communications in nonlinear analysis

30. ISRN applied Mathematics

31. Journal of Numerical Analysis and Approximation
Theory

32. Journal of Applied Mathematics and
Informatics.

33. Columbia International Publishing
(CIP).

34. Transactions on Mathematical Programming
and Applications.

35. Journal of Algorithms and
Optimization (jao@academicpub.org)

36. Journal of Pure and Applied Mathematics:
Advances and Applications (ISSN No:0974-9381) (scientificadvances.co.in/?cmd=journalandj=5)

37. Advances and Applications in Mathematical
Sciences (ISSN No:0974-6803) (mililink.com)

38. Arab Journal of Mathematics and Mathematical Sciences
(republication.com/editorial_board_of_ajmms.htm)

39. Mathematics Applied in Science and
Technology (republication.com/mast.htm)

__(C) ____Book and Grant Reviewer__

1. *Elementary Numerical Analysis* by Kendall Atkinson, University of
Iowa, published in 1992 by John Wiley & Sons.

2. *Moduli of Continuity and Global
Smoothness Preservation in Approximation Theory*. Reviewed for Springer-Verlag Publishers, World Scientific Publishing Company,
Elsevier Sciences B.V., Birkhauser, and CRC Press, 1998.

3. *A Handbook on Analytic-Computational
Methods and Applications*. Reviewed for Plenum Publ. Corp., World Scientific Publishing Company,
1999.

4. *Proklu's Comments on the First Book
of Euclid.* Vol. 2,
ISBN 960-8333-008, 2002, Evangelos Spandagos. I wrote the Introduction in
English, AITHRA Publ., Athens, Greece.

5. *College Algebra*, 4th Edition, 2003 by Aufmann,
Barker, Nation published by Houghton Mifflin.

6. On behalf of the U.S. Civilian
Research and Development Foundation (CRDF) located in Washington D.C. Grant Proposal
#12476 entitled: *Optimal methods for computing
singular integrals, solving singular integrals and applications to geophysics
and wave scattering of small bodies of arbitrary shapes *(2003)(Russian Federation).

7. On behalf of Duxbury Press, CA, USA,
the draft of the textbook “Statistical Literacy for Citizen(tentative
title)”, by Daniel Schaffer. My report was submitted in November, 2004.

8. On behalf of Springer-Verlag(Lecture
Series) the textbook entitled:”Iterative Approximation of Fixed
Points”by Vasile Berinde.

9. On behalf of U.S. Civilian Research
and Development Foundation(CRDF) Grant Proposal #144038,144002,144009,144015.My
id # is 17603.Contact: Jennifer MacNair, Staff Assistant Cooperative Grants
Program(Serbian Republic).

10. On behalf of U.S. Civilian Research
and Development Foundation (CRDF) Grant Proposal #15909, Fall 2006.

11. On behalf of Wiley and Sons Publ. Co.
For possible publication: Undergraduate book Entitled: ”Trigonometry”
by Cynthia Young., 2007.

12. On behalf of Wiley and Sons, Publ.
Co.For possible publication: Undergraduate book, entitled: “Algebra and
Trigonometry by Cynthia Young, 2007.

13. On behalf of (CRDF) Grant Proposal
#15912,Fall 2007.

14. On behalf of Prentice Hall Publ. Co.
For possible publication,Undergraduate book,entitled: “College Algebra:
by Barnett,Ziegler and Byleen, eighth
edition, Spring 2007.

15. Fondecyt-Proposal 1095025 .On behalf
of the Chilean government Author Dr. Sergio Plaza, Contact Maria Elena Boisier
,and Eriac Saavedra Mathematics Project coordinators,email:https://evalcyt.conicyt.cl,and esaavedra@conicyt.cl, October 27, 2008.

16. On behalf of the Republic of Serbia,
Ministry of Science and Technological Development. Grant Proposal Reviewer .
Project Number ON174025.Project Name:Problems in Nonlinear Analysis,operator,Theory,Topology
and Applications ,Investigator Dr. Vladimir Rakocevic.

17. On behalf of Wiley and Sons
Publ.Reviewed the book :The Heart of Mathematics:An Invitation to
EffectiveThinking,by E. Burger and M. Strabird
,Fall 2012.The book appeared in 2013.

18. On behalf of the Estonian Science
Foundation (ETAg-www.etag.ee). Post Doctoral Grant, Proposal: PUTJD17, Dr.
Indrek Zolk, Title: Nonlinear Functional Analysis (Fall 2013).

19. On behalf of KACST (Research
competitiveness program American Association for the advancement of Science) I reviewed 7 grant
proposals.

20. On behalf of the National Center for Science and
Technology Evaluation ,Ministry of Education and Science Astana,Republic of Kazakhstan. I reviewed 11
grant proposals.

__(D) ____Scientific Papers Reviewer__

I have reviewed a total of 435 papers for:

1. *Journal of Computational and Applied Mathematics*

2. *Punjab University Journal of Mathematics*

3. *Mathematica Slovaca*

4. *Pure Mathematics and Applications *(PUMA)

5. *Southwest Journal of Pure and Applied
Mathematics*

6. *IMA Journal of Numerical Analysis*

7. *Journal of Optimization Theory and
Its Applications*

8. *Computer Physics Communications*

9. *SIAM Journal on Numerical Analysis*

10. *Computational and Applied Mathematics*, CAM 97, 98, 99, Edmond, OK, USA

11. *Applied Mathematics Letters*

12. *Illinois Journal of Mathematics*

13. *Korean Journal of Computational and
Applied Mathematics*

14. *Proceeding of the Cambridge Mathematical
Society*

15. *Applicable Analysis*

16. *Journal of Applied Mathematics and
Optimization*

17. *Computers and Mathematics with
Applications*

18. *Computational and Applied Mathematics*

19. *Computational Analysis and
Applications*

20. *Tamkang Journal of Mathematics*

21. *Soochow Journal of Mathematics*

22. *Portugaliae Mathematica*

23. *Aequationes Mathematicae*

24. *Advances in Nonlinear Variational
Inequalities *(ANVI)

25. *Journal of Mathematical Analysis and
Applications*

26. *Journal of Complexity*

27. *SIAM Journal of Scientific Computing*

28. *International Journal of Mathematics
and Mathematical Sciences*

29. *AMS Mathematics of Computation*

30. *BIT, Numerical Mathematics*

31. *Applied Analysis*

*32. **Journal of Applied Mathematics and
Computing*

*33. **Central European Journal of Mathematics*

*34. **Applied Numerical Mathematics*

*35. **Korean Journal of Mathematics in
Education*

*36. **Journal of Integral Equations with
Applications*

*37. **Bulletin of The Malaysian Mathematical
Society*

*38. **Acta Mathematica Sinica*

*39. **Electronic Journal of Differential
Equations *

*40. **Studia Mathematica Hungarica*

*41. **Mathematical Reviews of the American Mathematical
Society*

*42. **Mathematics of Computation of the
American Mathematical Society*

*43. **PUJM*

*44. **International Journal of Computer Mathematics*

*45. **Zhejiang University Journal of Mathematics*

*46. **Physics Letters A.*

*47. **Numerical Algorithms*

*48. **Journal of Inequalities and
Applications*

*49. **Proceedings of the American Mathematical
Society*

*50. **Journal of Applied Mathematics and
Stochastic Analysis*

*51. **Fixed Point Theory and Applications*

*52. **Applicationes Mathematicae*

*53. **European Journal of Operations
Research.*

*54. **Nonlinear Analysis*

*55. **Fuzzy sets and systems*

*56. **American Mathematical Monthly*

*57. **Mathematical Inequalities and Applications*

*58. **Journal of Mathematical
Sciences:Advances and Applications*

*59. **SINUM*

*60. **Archivum Mathematicarum*

*61. **Applied Mathematics and Computation*

*62. **Numerical Functional Analysis and
Optimization*

*63. **Applied Mathematics A..J.Chinese
University*

*64. **Fixed Point Theory and Applications*

*65. **MPE (Hindawi)*

*66. **Journal of Inequalities and
Applications*

*67. **Albanian Journal of Mathematics*

*68. **Optimization*

*69. **Europen Journal of Operations
Research*

*70. **Mathematica Slovaca*

*71. **Cubo*

*72. **Computational Methods in Applied Mathematics*

*73. **Hacettepe Journal of Mathematics and
Stataistics*

*74. **Applied Numerical Mathematics*

*75. **Kuwait Journal of Science and
Engineering*

*76. ** ISRN Journal of Applied Mathematics*

*77. **Advances in Difference Equations*

*78. **Journal of Mathematical Sciences and
Advances with applications.*

*79. **Indian Journal of Pure and Applied Mathematics*

*80. **Advances and Applications in Mathematical
Sciences*

*81. **Journal of Inequalities and
Applications.*

*82. **CANA*

*83. **Siam Journal of Mathematical Analysis*

*84. **Mathematical Modelling and Analysis.*

__(E) ____Grants Received__

1. New Mexico State University Grant, (1986), #1-3-43841, RC #87-01

2. New Mexico State University Grant, (1987), #1-3-4-44770.

3. U.S.A. Army (1988-1990), #DAEA, 26-87-R-0013 (F.M.) Army (jointly with the Mechanical Engineering Department at New Mexico State University). Topic: "Solution of differential equations on parallel computers"

4. Cameron University, Research support,
July 1992, June 1998

5. Cameron University, Academic
Initiatives Award (#6110), 2004-2005.

6. NSF 2007 EPSCOR INFRASTRUCTURE
IMPROVEMENT PROPOSAL Participant (Leading Investigator Dr. Henry Neeman).

7. Received CU grant 120006 for
2014-2015 ( For undergraduate
research)..

__(F) ____Supervising Graduate Students__

1. The following Ph.D. students have obtained their Ph.D. degree under my supervision:

2. Losta Mansor, Ph.D. dissertation
title: Numerical Methods for Solving Perturbation Problems Appearing in
Elasticity and Astrophysics, 1989

3. Joan Peeples, Ph.D. dissertation
title: Point to Set Mappings and Oligopoly Theory, 1989 Member, Doctoral
Examination Committee:

4. Aomar Ibenbrahim, Spring 1987

5. Maragoudakis Christos, Spring 1988 (Dean's Representative for both, Electrical Engineering Department)

6. Bellal Hossain, Fall 1996, University of Calcutta, India

7. Sri Pulak Guhathakurta, Spring 1998, University of Calcutta, India

8. Tariq Iqtadar Khan, Spring 2003,
Aligarh University, India

9. Landlay Khan,Fall 2005, Aligarg
University,India,Thesis title:Common Fixed Point Theorems for some families of
nonself mappings in metrically convex spaces.

10. Nadeem Ahmad, Summer 2007, Ph. D.
Thesis external supervisor,Thesis title:Geometric Modelling using subdivision
techniques, PUJM, Lahore Pakistan.

11. Syed Abbas ,Fall 2009,Ph.D. Thesis
Title: Almost periodic solutions of nonlinear functional differential
equations,Indian Institute of Technology Kanpur, India.

12. Kashif Rehan, Spring 2010,Phd.
Thesis:Subdivision Schemes:The new paradigm in computer aided geometric design.
University of Punjab ,Lahore Pakistan.

13. Goutam Sarmar, Spring 2012, Some
development of numerical methods for solving ODE. University of Kalyani, India.

14. H. U. Rehman, Fall 2013. Ph. D.
Thesis: Use of Reproducing Kernel Hilbert space functions to solve boundary
value problems. University of the Punjab, Lahore, Pahistan.

15. Susanta Kumar Mohanta,Fall
2014,Ph.D Thesis: A study of nonlinear
variational problems in various spaces,KIIT University,Orissa,India.

16. H.M.Asim Zafar,Spring
2014,Ph.D.Thesis:The action of Hecke groups on real and imaginary quadratic
fields.University of the Punjab,Lahore
Pakistan.

17. Izhar Udin, Fall 2014,Ph.D.Thesis:A
study of fixed point theorems in Banach and Cat(o) spaces.,Aligarh Muslim
University,Aligragh ,India.

18. Saima Arshed,Spring 2015,Numerical
solution of partial Differential Equations Using B-Spline,University of the
Punjab,Lahore Pakistan.

**Chair, Master's
Examination Committee**

1. Mitra Ashan, Spring 1987

2. Christopher Stuart, Spring 1988

3. Anis Shahrour, Fall 1988

**Member, Master's
Examination Committee**

1. Juji Hiratsuka, Spring 1987 (Dean's Representative, Art Department)

2. Alice Lynn Bertini, Spring 1988

3. Daniel Patrick Eshner, Summer 1989 (Dean's Representative, Computer Science)

__(G) ____Committee Member for Hiring-Promotion-Tenure__

I have served as a committee member for:

(a) Hiring: Cameron University (USA), every year, Punjab University (Pakistan), 2000 and 2002

(b) Promotion-Tenure: Cameron University (USA), Sultan Qaboos University, Sultanate of Oman, Sam Houston State University (USA), Punjab University (Pakistan), 2001

(c) Promotion Dr. Marwan S. Abualrub,University of Jordan,2011.

(d) Ternure: Dr. Siddiqi, University of the Punjab, Lahore, Pakistan, 2013.

__(H) ____M. Sc. and Ph. D. Dissertations__

1. A Contribution to the Theory of Nonlinear Operator Equations in Banach Space, Master of Science Dissertation, University of Georgia, GA, U.S.A., 1983.

2. Quadratic Equations in Banach Spaces, Perturbation Techniques and Applications to Chandrasekhar's and Related Equations, Doctor of Philosophy Dissertation, University of Georgia, GA, U.S.A., 1984.

__(I) ____Books and Monographs Published__

1. *The Theory and Applications of
Iteration Methods*,
CRC Press, Inc., Systems Engineering Series, Boca Raton, Florida, 1993, Math.
Rev. 65b:65001, Zbl. Math. 65J, 65052, (W.C. Rheinboldt (Pittsburgh)), (1992),
844-441, ISBN 0-8493-8014-6. (Textbook)

2. *A Unified Approach for Solving
Nonlinear Operator Equations and Applications*, West University of Timisoara, Department of Mathematics,
Mathematical Monographs, 62, Publishing House of the University of Timisoara,
Timisoara, 1997, AMS Math. Reviews 99i65060. (Monograph)

3. *The Theory and Application of
Abstract Polynomial Equations*, St. Lucie/CRC/Lewis Publishers, Mathematics Series, Boca
Raton, Florida, USA, 1998, ISBN 0-8493-8702-7. Springer-Verlag Publ., New York
is publishing this text since 2000 by taking over from CRC. (Textbook), MR
1818212

4. *Dictionary of Comprehensive
Dictionary of Mathematics: Analysis, Calculus and* *Differential
Equations*, (Contributing Author), Editor: Douglas, N. Clark, Chapman-Hall/CRC/Lewis
Publishers, Boca Raton, Florida, USA, 1999, ISBN 0-8493-0320-6. (Textbook)

5. *Computational Methods for Abstract
Polynomial Equations*,
West University of Timisoara, Department of Mathematics, Mathematical
Monographs, 68, Publishing House of the University of Timisoara, Timisoara,
1999. (Monograph), MR 1997218

6. *A Survey of Efficient Numerical
Methods for Solving Equations and Applications*, Kyung Moon Publishers, Seoul,
Korea, 2000, ISBN 8972824828. (Textbook)

7. *A Unified Approach for Solving
Equations, Part I: On Infinite-Dimensional Spaces*, Handbook of Analytic Computational
Methods in Applied Mathematics, Chapman and Hall/CRC Press, Inc., Boca Raton,
Florida, 2000, Chapter 5, pp. 201-254, ISBN 1-58488-135-6. (Monograph)

8. *A Unified Approach for Solving
Equations, Part II: On Finite-Dimensional Spaces*, Handbook on Analytic Computational
Methods in Applied Mathematics, Chapman and Hall/CRC Press, Inc., Boca Raton,
Florida, 2000, Chapter 6, pp. 255-308, ISBN 1-58488-135-6. (Monograph)

9. *Two Contemporary Computational
Aspects of Numerical Analysis*, Applied Math. Reviews, Volume 1, World Scientific
Publishing Corp., River Edge, NJ, 2000, ISBN 981-02-4339-1.
(Monograph)

10. *Advances in the Efficiency of Computational
Methods and Applications*, World Scientific Publ. Co., River Edge, NJ, 2000, ISBN 981-02-4336-7.
(Textbook)

11. *Iterative Methods for Solving
Equations Appearing in Engineering and Economics. *Kyung Moon Publ., Seoul, Korea, 2001,
ISBN 89-7282-512-3. (Textbook)

12. *Contemporary Computational Methods in
Numerical Analysis, Part I. Methods Involving Fréchet-Differentiable
Operators of Order One, *Mathematical Monographs (Timisoara), **74**, West University of Timisoara, Department of Mathematics,
Publishing House of the University of Timisoara, Timisoara, Romania,2002
viii+170 pp, MR 2053593(2005a:65051a), (Monograph).

13. *Contemporary Computational Methods in
Numerical Analysis, Part II: Methods Involving Fréchet-Differentiable
Operators of Order m (m > 2),
*Mathematical
Monographs (Timişoara),

14. Newton Methods, Nova Science
Publ.Corp., Hauppauge, New York, USA, 2005, ISBN:1-59454-052-7,(Textbook).

15. Approximate Solution of Operator Equations
with Applications, World Scientific Publ. Co.,Pte.Ltd.,Hackensack,NJ,2005,USA,ISBN:981-256-365-2,
512 pages (Textbook).

16. Computational Theory of Iterative
Methods, Series: Studies in Computational Mathematics 15, Editors, ;C. K. Chui,
and L. Wuytack, Elsevier Publ. Co., New York, USA, 2007, (Textbook), ISBN
978-0-444-53162-9.

17. Convergence and applications of
Newton-type iterations, Springer –Verlag
Publ., 2008, ISBN-13:978-0-387-72741-7e and ISBN-13:978-0-387-72743-1.

18. Efficient methods for solving
equations and variational inequalities, Polimetrica
Publ. Comp., 2009, 603 pages, ISBN: 978-88-7699-149-3

19. Aspects of computational theory for certain
iterative methods, Polimetrica Publ. Comp., 2009, 571 pages, ISBN: 978-88-7699-151-6.

20. Mathematical Modelling with Applications in Biosciences,
and Engineering, Nova Science Publ. Corp., Hauppauge, New York, USA, 2011, ISBN
978-61728-944-6

21. Advances on iterative procedures,
Nova Science Publ. Corp. Hauppauge, New York, USA, 2011, ISBN
978-1-61209-522-6.

22. Numerical methods for equations and
its applications, CRC Press/Taylor and Francis Group, New York 2012, ISBN: 978-1-57808-753-2.

23. Computational Methods in Nonlinear
Analysis,Efficient Algorithms,Fixed point theory and applications,World
Scientific Publ.Comp.ISBN-9789814405829,New Jerssey,2013 .

24. Iterative methods for nonlinear
equations or systems and their applications 2013,Journal of Applied Mathematics,
Co-Editor, Hindawi Publ.ISSN:1110-757X,ISBN:2 370000125989,2013.

25. Iterative methods for nonlinear
equations or systems of equations and their applications,2014,Journal of
Applied Mathematics, Co-Editor, Hindawi Publ.

__Books and Monographs
Under Preparation/Accepted__

26.

__(J1) UNDERGRADUATE
RESEARCH__

**(1) Geneva Howard, Masters
student in Education, Math 4492, (Independent study), Spring 2003.**

**Paper Title: Linear
Programming in Mathematics Education.**

**Poster Presentation, Oklahoma
Research Day, 2003, Edmond Oklahoma**

**(2) Martina Melrose, Math 4493
(independent study), Spring 2004.**

**Paper title: Linear and
Nonlinear Programming survey.**

**Poster Presentation, Oklahoma
Research Day 2004, Edmond Oklahoma.**

**(3) Ivica Ristovski, Spring 2005.**

**Paper Title: On an
inequality from Applied Analysis**

**Paper Presentation at the
Torus conference, February 25, 2005.**

**(4)
****Gabriel Vidal**

**Paper title: Observations on
Newton’s method.**

**Poster Presentation, Oklahoma
Research Day 2005, Edmond Oklahoma, November 11.**

**(5)
**** Irene Corriette and Ms Sabina Sadou**

**Paper Title: Advances on
Newton’s method.**

**Poster Presentation, Okalhoma
Research Day 2006, November 20, Edmond Oklahoma.**

**(6) Jingshu Zhao,**

**Paper Title: Applications of
sequences and series to numerical methods.**

**Paper Presentation, Oklahoma
Research Day 2009, Oklahoma**

**(7)
****Jingshu Zhao**

**Paper Presentation, Torus
Conference, Wichita Falls, February 27, 2010.**

**(8)
****Shobhakhar
Adhikari**

**Poster Presentation,
Oklahoma Research Day 2010 CU, Lawton, OK November 12 ,2010.**

**Poster Presentation,
Oklahoma Research Day 2011,CU Lawton, OK October ,2011.**

**(9)
****Daniel Ijigbamigbe**

**Poster Presentation,
Oklahoma Research Day 2013, March 8, 2013.**

**(10)**** Akinola Akinlawon **

**Poster Presentation: Oklahoma Research Day
2014, March 2014**

**(11)Akinola Akinlawon**

**Paper Submission:Oklahoma Undergraduate
Research Journal,Fall 2014 **

**Poster Presentation:Oklahoma Research
Day2015,March 2015**

__(J2) RESEARCH ARTICLES__

The scientific papers listed below have been published in the following countries and at the top refereed journals in the following countries repeatedly:

*America***: **U.S.A., Brazil, Canada, Chile

**Europe****: **U.K.,
Sweden, Belgium, Holland, Spain, Germany, Austria, Hungary, Slovakia, Romania, Poland, Yugoslavia, Italy, Chech Republic,Bulgaria

**Asia: **People's Republic of
China, Republic of China, India, Pakistan, Japan, Saudi Arabia, Korea,
Singapore, Malaysia

**Australia****: **Australia

1.
Quadratic
equations and applications to Chandrasekhar's and related equations, ** Bull. Austral. Math. Soc.**, Vol.
32, 2 (1985), 275-292;

2.
On a contraction theorem and applications, *Proc. Amer. Math. Soc.**, *1983,* ***45**, 1 (1986), 51-53; Math. Rev.
87h: 65108, Sh. Singh, Z.F.M.6224077 (1988).

3.
Iterations
converging to distinct solutions of some nonlinear equations in Banach space, ** Inter. J. Math. Math. Sci.**, Vol.
9, No. 3 (1986), 585--587; Z.F.M.61447044 (1986); Math. Rev. 87j47097, P.P.
Zabrejko (Minsk).

4.
On
the cardinality of solutions of multilinear differential equations and
applications, ** Internat. J. Math. Math.
Sci.**, Vol. 9, No. 4 (1986), 757-766; Math. Rev. 88e34017, Achmadjon
Soleev (Samarkand); Z.F.M.66334008 (89), A. Soleev.

5.
Uniqueness-Existence of solutions of polynomial equations in
linear space, ** Punj. Univ. J. Math.** Vol. XIX (1986), 39-57;
Z.F.M.62547050 (1988); Math. Rev.88g47116, B.G. Pachpatte (6-Mara).

6.
On
a theorem for finding "large" solutions of multilinear equations in
Banach space, ** Punj. Univ. J. Math.**,
Vol. XIX (1986), 29-37; Z.F.M.62547051 (1988); Math.Rev. 88g47115, B.G.
Pachpatte (6-Mara).

7.
On the approximation of some nonlinear equations, ** Aequationes Mathematicae**,

8.
An improved condition for solving multilinear equations, ** Punj. Univ. J. Math.**, Vol. XX (1987), 43-46; Math. Rev. 89c47065;
Z.F.M.64747015, (1989).

9.
On a class of nonlinear equations, *Tamkang J. Math***.**, Vol. 18,
No. 2 (1987); 19-25; Math. Rev. 89f47091, Ramendra Krishna Bose (1-SUNYF);
Z.F.M.65347042, (1989), J. Appel.

10.
On
polynomial equations in Banach space, perturbations, techniques and
applications, ** Internat. J. Math. Math.
Sci.**, Vol. 10, No. 1 (1987), 69-78; Math. Rev. 88c47123, Heinrich
Steinlein (Munich); Z.F.M.61747038, (1987).

11.
A note on quadratic equations in Banach space, ** Punj. Univ. J. Math.**, Vol. XX (1987), 47-50; Math. Rev. 89c47076;
Z.F.M.64747016, (1989).

12.
Quadratic finite rank operator equations in Banach space, *Tamkang J. Math***.**, Vol. 18, No. 4 (1987); 8-19;
Z.F.M.66247011 (89); Math. Rev. 89k47100, Nicole Brillouet-Belluot (Nantes).

13.
On some theorems of Mishra Ciric and Iseki, ** Mat. Vesnik**, Vol. 39 (1987), 377-380; Math. Rev. 89c54083;
Z.F.M.64854035, (1989).

14.
An iterative solution of the polynomial equation in Banach space, *Bull. Inst. Math. Acad. Sin***.**, Vol. 15,
No. 4 (1987), 403-410; (Math. Rev. Author index 1989), 47H17, 46G99, 58C15.

15.
A
survey on the ideals of the space of bounded linear operators on a separable
Hilbert space, *Rev. Acad. Ci. *** Exactas Fis. Quim. Nat. Zaragoza**, II.
Ser. 42 (1987), 24-43; Math. Rev. 89g47059.

16.
On the solution by series of some nonlinear equations, *Rev. Acad. Ci. *** Exactas Fis. Quim.Nat. Zaragoza**, II. Ser. 42
(1987), 18-23; Z.F.M.64947048, (1989); Math. Rev. 90f65085, V.V. Vasin (Sverdlosk).

17.
Newton-like methods under mild differentiability conditions with
error analysis, *Bull. Austral***. Math. Soc.**, Vol. 37, 1 (1988), 131-147; Z.F.M.62965061, (1988), S. Reich; Math.
Rev. 89b65142, A.V. Dzhishkariani (Tbilisi).

18.
On Newton's method and nondiscrete Mathematical induction, *Bull. Austral. Math. Soc***.**, Vol. 38 (1988), 131-140; Math. Rev.
90a65136, A.M. Galperin (Ben-Gurion Intern. Airp.).

19.
On a class of nonlinear integral equations arising in neutron
transport, ** Aequationes Mathematicae**, Vol. 35 (1988), 99-111; Math. Rev.
89M47058, H.E. Gollwitzer (1-DREX).

20.
New ways for finding solutions of polynomial equations in Banach
space, *Tamkang J. Math***.**, Vol. 19, 1 (1988), 37-42; Math.
Rev. 90f47093, V.V. Vasin (Sverdlosk).

21.
On a new iteration for solving polynomial equations in Banach
space**, **** Funct. Approx. Comment. Math.**, Vol. XIX (1988); Math. Rev. 91d:65082, Xiaojun Chen.

22.
Conditions
for faster convergence of contraction sequences to the fixed points of some
equations in Banach space, ** Tamkang J. Math.**, Vol. 19, 3
(1988), 19-22; Math. Rev. 90j47074, Roman Manka (Mogilno).

23.
Approximating the fixed points of some nonlinear equations, ** Mathem. Slovaca**,

24.
Some
sufficient conditions for finding a second solution of the quadratic equation
in Banach space, ** Mathem. Slovaca**,

25.
Concerning
the approximation solutions of operator equations in Hilbert space under mild differentiability conditions, ** Tamkang J. Math.**, Vol. 19, No. 4 (1988), 81-87; Math. Rev.
91g:65137, P.S. Milojevic.

26.
The Secant method and fixed points of nonlinear equations, ** Monatshefte fur Mathematik**,

27.
An
iterative procedure for finding "large" solutions of the quadratic
equation in Banach space, ** Punj. Univ.
J. Math.**, Vol. XXI (1988), 13-21; Math. Rev. 91g:65136, P.S. Milojevic.

28.
Vietta-Like relations in Banach space, *Rev. Acad. Ci. *** Exactas Fis. Quim. Nat. Zaragoza**, I,
Ser. 43 (1988), 103-107; Math. Rev. 47f47095, V.V. Vasin (Sverdlovsk).

29.
A global theorem for the solutions of polynomial equations, ** Rev. Acad. Ci. Exactas Fis. Quim. Nat Zaragoza**, I, Ser. 43 (1988), 93-101; Math. Rev. 90f47094, V.V. Vasin,
(Sverdlosk).

30.
Concerning the convergence of Newton's method, ** Punj. Univ. J. Math.**, Vol. XXI (1988), 1-11; Math. Rev. 91g:65135, P.S.
Milojevic.

31.
On the number of solutions of some integral equations arising in
radiative transfer, *Internat.*** J. Math.& Math. Sci.**, Vol. 12, No. 2 (1989), 297-304; Math.
Rev. 90h86004, S. Rajasekar (Ticuchirapalli).

32.
On the approximate solutions of operator equations in Hilbert
space under mild differentiability conditions, *J. Pure Appl. Sci***.**, Vol. 8, No.
1 (1989), 51-56.

33.
On the fixed points of some compact operator equations, *Tamkang J. Math***.**, Vol. 20, No. 3 (1989), 203-209; Math. Rev. 91a47088,
Jing Xian Sum (PRC-Shan).

34.
Error bounds for a certain class of Newton-like methods, *Tamkang J. Math***.**, Vol. 20, No. 4 (1989); Math. Rev. 91k:65096, J.W. Schmidt.

35.
Concerning
the convergence of iterates to fixed points of nonlinear equations in Banach space, ** Bull.
Malays. Math. Soc.**, Vol. 12, 2 (1989), 15-24; Math. Rev. Author index
1991.

36.
A series solution of the quadratic equation in Banach space, *Chinese J. Math***.**, Vol. 27, No. 4 (1989); Math. Rev. 90k47131.

37.
On a fixed point in a 2-Banach space, *Rev. Acad. *** Ciencias, Zaragoza**,

38.
Some matrices in oligopoly theory, *New Mexico J. Sci***.**, **29**,
1 (1989), 22.

39.
On a theorem of Fisher and Khan**, ***Rev. Acad. *** Ciencias, Zaragoza**,

40.
On quadratic equations*, **Anal. Numér. Théor. Approx*., **18**, 1 (1989), 19-26; Math. Rev. 91f:47094.Concerning the approximate solutions
of nonlinear functional equations under mild differentiability
conditions, ** Bull. Malays. Math.
Soc.**, Vol. 12, 1 (1989), 55-65; Math. Rev. 91k:47164, V.V. Vasin.

41.
On the convergence of certain iterations to the fixed points of
nonlinear equations, *Annales
sectio computatorica, Ann. Univ. Sci.
Budapest. Sect. Computing*,

42.
On the secant method and nondiscrete mathematical induction, *Anal. Numér. Théor. Approx*.*, *tome **18**, No. 1 (1989), 27-36; Math.
Rev. 91j:65104.

43.
On Newton's method for solving nonlinear equations and multilinear
projections, *Functiones et
approximatio Comment. Math***.**, **XIX** (1990), 41-52; Math.
Rev. 92b:4707, Joe Thrash.

44.
Nonlinear operator equations and pointwise convergence, *Functiones et approximatio Comment. Math***.**, **XIX**
(1990), 29-39; Math. Rev. 92b:47106, Joe Thrash.

45.
Iterations
converging faster than Newton's method to the solutions of nonlinear equations in Banach space, ** Functiones et approximatio Comment. Math.**,

46.
On some quadratic integral equations, ** Functiones et
Approximmatio**,

47.
A
mesh independence principle for nonlinear equations using Newton's method and
nonlinear projections, ** Rev. Acad. Ciencias. Zaragoza**,

48.
Error bounds for the modified secant method, ** BIT**,

49.
Improved error bounds for a certain class of Newton-like methods**, **** J. Approx. Theory Appl.**, (6:1) (1990), 80-98; Math. Rev. 92a:65188, A.M. Galperin.

50.
On the solution of some equations satisfying certain differential
equations, *Punj. Univ. J. Math***.**, Vol. XXIII
(1990), 47-59; Math. Rev. 92d:65102.

51.
On
some projection methods for approximating the fixed points of nonlinear
equations in Banach space, ** Tamkang J. Math.**, Vol. 21, 4
(1990), 351--357; Math. Rev. 92a:47072, Joe Thrash.

52.
On some projection methods for the approximation of implicit
functions, *Appl. Math. Lett***.**, Vol. 3, No.
2 (1990), 5-7; Math. Rev. 91b65066.

53.
On
the monotone convergence of some iterative procedures in partially ordered
Banach spaces, ** Tamkang J. Math.**,
Vol. 21, No. 3 (1990), 269-277; Math. Rev. 91h:47067, Joe Thrash.

54.
The
Newton-Kantorovich method under mild differentiability conditions and the Ptak
error estimates, ** Monatschefte fur Mathematik**, Vol. 109, No. 3 (1990); Math.
Rev. 91k:65034, J.W. Schmidt.

55.
The secant method in generalized Banach spaces, *Appl. Math. Comput***.**, **39** (1990), 111-121; Math. Rev.
91h:65099.

56.
On the solution of equations with nondifferentiable operators and
Ptak error estimates, ** BIT**,

57.
On some projection methods for enclosing the root of a nonlinear
operator equation, ** Punj. Univ. J. Math.**, Vol. XXIII (1990), 35-46; Math.
Rev. 91h:47067, Joe Thrash.

58.
A
mesh independence principle for operator equations and their discretizations
under mild differentiability conditions, ** Computing**,

59.
On Newton's method under mild differentiability conditions, *Arabian J. Math***.**, Vol. 15, 1 (1990), 233-239; Math.
Rev. 91k:65097, J.W. Schmidt.

60.
Remarks on quadratic equations in Banach space, *Intern. J. Math. Math. Sci***.**, Vol. 13, No. 3 (1990), 611-616; Math.
Rev. 91e:47062.

61.
On
the improvement of the speed of convergence of some iterations converging to
solutions of quadratic equations, ** Acta Math. Hungarica**, Vol.
57/3-4 (1990), 245-252; Math. Rev. 93d:47121, Teodor Potra.

62.
A note on Newton's method, *Rev. Acad. *** Ciencias Zaragoza**,

63.
On the solution of compact linear and quadratic operator equations
in Hilbert space, *Rev. Acad***. Ciencias Zaragoza**,

64.
On
some generalized projection methods for solving nonlinear operator equations
with a nondifferentiable term, ** Bull. Malays. Math. J.**, Vol. 13,
No. 2 (1990), 85-91; Math. Rev. 92g:65065, Gerard, Lebourg.

65.
Comparison theorems for algorithmic models, *Appl. Math. Comput***.**, Vol. 40, No. 2 (Nov. 1990), 179-187; Math. Rev. 92b:65102.

66.
On an iterative algorithm for solving nonlinear equations, *Beitrage zur Numerischen Math***.** (Renamed
Z.A.A.), Vol. 10, No. 1 (1991), 83-92; Math. Rev. 93b:47132.

67.
On
time dependent multistep dynamic processes with set valued iteration functions
on partially ordered topological spaces, ** Bull. Austral. Math. Soc.**, Vol.
43 (1991), 51-61; Math. Rev. 92d:65107, Tetsuro Yamamoto.

68.
Error bounds for the secant method, ** Math. Slovaca**, Vol. 41, 1 (1991), 69-82; Math.
Rev. 92j:65086, K. Bohmer.

69.
On
the approximate solutions of nonlinear functional equations under mild
differentiability conditions, ** Acta Math. Hungarica**, Vol. 58
(1-2) (1991), 3-7; Math. Rev. Author index, 1992.

70.
On the convergence of some projection methods with perturbation, *J. Comput. Appl. Math***.**, **36** (1991), 255-258; Math.
Rev. 92f:65065, H.R. Shen.

71.
On
an application of a modification of the Zincenko method to the approximation of
implicit functions, ** Z.A.A.**,

72.
On
some projection methods for solving nonlinear operator equations with a
nondifferentiable term, ** Rev. Academia de Ciencias, Zaragoza**,

73.
Integral equations for two-point boundary value problems, *Rev. Academia de Ciencias**, Zaragoza*,

74.
A fixed point theorem for orbitally continuous functions, *Pr. Rev. Mat***.**, Vol. 10, No. 7 (1991), 53-57; Math.
Rev. 93d:47101, Ramendra Krishna Bose.

75.
Bounds for the zeros of polynomials, ** Rev. Academia de
Ciencias, Zaragoza**,

76.
On a class of quadratic equations with perturbation**, **** Functiones et
Approximmatio**,

77.
On
a new iteration for finding "almost" all solutions of the quadratic
equation in Banach space, ** Studia Scientiarum Mathematicarum Hungarica**,

78.
A Newton-like method for solving nonlinear equations in Banach
space, ** Studia Scientiarum Mathematicarum Hungarica**,

79.
On the convergence of nonstationary Newton methods, *Func. et Approx***.**, Vol. XXI (1992), 7-16; Math. Rev.
95g:65080, A.M. Galperin.

80.
On
an application of the Zincenko method to the approximation of implicit
functions, ** Publicationes Mathematicae
Debrecen**, Vol. 40/1-2 (1992), 43-49; Math. Rev. 93c:47076, A.M.
Galperin.

81.
Improved error bounds for the modified secant method, *Intern. J. Computer Math***.**, Vol. 43, No. 1+2 (1992), 99-109.

82.
On
the midpoint method for solving nonlinear operator equations in Banach spaces, ** Appl. Math. Letters**, Vol. 5, No.
4 (1992), 7-9; Math. Rev. 96b:65061.

83.
On an application of a Newton-like method to the approximation of
implicit functions, ** Math. Slovaca**,

84.
On the monotone convergence of general Newton-like methods, *Bull. Austral. Math. Soc***.**, **45** (1992), 489-502; Math.
Rev. 93c:65077.

85.
Convergence of general iteration schemes, *J. Math. Anal. Appl***.**, **168**, No. 1 (1992), 42-52; Math.
Rev. 93d:65055, S. Sridhar.

86.
Some generalized projection methods for solving operator
equations, *J. Comp. Appl. Math***.**, **39**,
No. 1 (1992), 1-6; Math. Rev. 92m:65079.

87.
Sharp
error bounds for a class of Newton-like methods under weak smoothness
assumptions, ** Bull. Austral. Math. Soc.**,

88.
Approximating Newton-like procedures, *Appl. Math. Lett***.,** Vol. 5, No.
1 (1992), 27-29. CMP 1 144362.

89.
On a mesh independence principle for operator equations and the
secant method, *Acta Math***. Hungarica**,

90.
On the solution of quadratic integral equations, *Punj. Univ. J. Math.,** *Vol. XXV (1992), 131-143; Math. Rev. 95j:65177, P.
Uba.

91.
On the convergence of generalized Newton-methods and implicit
functions, *J. Comp***. Appl. Math.**,

92.
On a Stirling-like method, *Punj. Univ. J. Math***.**, Vol. XXV
(1992), 83-94; Math. Rev. 95j:65062, Anton Suhadolc.

93.
On the approximate construction of implicit functions and Ptak
error estimates, *Punj. Univ. J. Math***.**, Vol. XXV
(1992), 95-98; Math. Rev. Author Index 1995.

94.
On
the numerical solution of linear perturbed two-point boundary value problems
with left, right and interior boundary layers,*
Arabian J. Science and Engineering*,

95.
On the convergence of Newton-like methods, *Tamkang J. Math***.**, Vol. 23, No. 3 (1992), 165-170; Math.
Rev. 93m:65077, J.W. Schmidt.

96.
On the monotone convergence of algorithmic models, *Appl. Math. Comput***.**, **48**, (2-3) (1992), 167-176; Math.
Rev. 92m:47134, Vincentiu Dumitru.

97.
Approximating Newton-like iterations in Banach space**, ***Punj. Univ. J. Math***.**, Vol. XXV
(1992), 49-59; Math. Rev. 95j:65061, Anton Suhadolc.

98.
On
the approximation of quadratic equations in Banach space using finite rank
operators, ** Rev. Academia de ciencias
Zaragoza**,

99.
Remarks
on the convergence of Newton's method under Holder continuity conditions, ** Tamkang J. Math.**, Vol. 23, No. 4
(1992), 269-277; Math. Rev. 94b:65080, J.W. Schmidt.

100. On the solution of nonlinear operator
equations in Banach space and their discretizations, ** Pure Math. Appl.**,

101. On the convergence of
optimization algorithms modeled by point-to-set mappings, *Pure Math. Appl.***, Ser. B**, Vol.
3, No. 2-3-4 (1992), 77-86; Math. Rev. 94i:90117, Han Ch'ing Lai.

102. On the convergence of
inexact Newton-like methods, ** Public. Math. Debrecen**, Vol. 43, 1-2 (1993), 79-85; Math.
Rev. 94h:65064, Carl T. Kelley.

103. On some projection methods for the
solution of nonlinear operator equations with nondifferentiable
operators, ** Tamkang J. Math.**,
Vol. 24, No. 1 (1993), 1-8; Math. Rev. 94m:65097, A.V. Dzhishkariani.

104. An initial value method for solving
singular perturbed two-point boundary value problems, ** Arabian Journ. Scienc. Engineer.**, Vol. 18, 1 (1993), 3-5.

105. On the solution of
nonlinear equations with a nondifferentiable term*, **Rev. Anal. Numér. Théor. Approx**.*, Tome **22**, 2
(1993), 125-135; Math. Rev. 96a:65092, A.M. Galperin (IL-BGUN; Be'er Sheva).

106. Some methods for finding error bounds
for Newton-like methods under mild differentiability conditions,
** Acta Math. Hungarica**,

107. On the secant method, ** Publicationes Mathematicae Debrecen**, Vol. 43, 3-4 (1993), 223-238; Math.
Rev. 95j:47077, R. Kodnar.

108. Improved error bounds for Newton's
method under generalized Zabrejko-Nguen-type assumptions,
** Appl. Math. Letters**,
Vol. 6, No. 3 (1993), 75-77; Math. Rev. Author index 1996.

109. A fourth order iterative
method in Banach spaces, ** Appl. Math. Letters**, Vol. 6, No. 4 (1993), 97-98; Math.
Rev. Author index 1996.

110. Newton-like methods and
nondiscrete Mathematical induction, ** Studia Sci. Math. Hung.**,

111. Robust estimation and
testing for general nonlinear regression models, *Appl. Math. Comp***.**, **58**
(1993), 85-101; Math. Rev. 94i:62097, Adrej Pazman.

112. A mesh independence
principle for nonlinear operator equations in Banach space and their
discretizations, ** Studia Sci. Math. Hung**.,

113. Sharp error bounds for
the secant method under weak assumptions, ** Punj. Univ. J. Math.**, Vol. XXVI (1993), 54-62; Math. Rev.
Author index 1995.

114. An error analysis of
Stirling's method in Banach spaces, *Tamkang J. Math***.,** Vol. 24,
No. 2 (1993), 115-133; Math. Rev. 94h:65058, A.M. Galperin.

115. New sufficient conditions for the approximation
of distinct solutions of the quadratic equation in
Banach space, *Tamkang J. Math.**,
*Vol. 24, No. 4 (1993), 355-372; Math. Rev. 95f:47090.

116. On the convergence of
inexact Newton methods, *Chinese J. Math***.**, Sept. Vol.
21, No. 3 (1993), 227-234; Math. Rev. 94f:47088, Mihai Turinici.

117. On the solution of
equations with nondifferentiable operators, *Tamkang J. Math***.**, Vol. 24,
No. 3 (1993), 237-249; Math. Rev. 94i:65070, C. Ilioi.

118. Sufficient conditions for
the convergence of general iteration schemes, *Chinese J. Math***.**, Vol. 21,
No. 2 (1993), 195-205; Math. Rev. 94f:47087, Mihai Turinici.

119. On a two-point Newton method in
Banach spaces of order four and applications, (1993), Proceedings of the 9th
Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), ** Rev. Academia de Ciencias, Zaragoza**,

120. On a two-point Newton method in
Banach spaces of order three and applications, Proceedings of the 9th Annual
Conference on Applied Mathematics, CAM 93, University of
Central Oklahoma, Edmond, (1993), 24-37; ** Punj. Univ. J. Math.**, Vol. 27 (1994), 10-22; Math. Rev.
Author index 1996.

121. On a two point Newton-method in
Banach spaces and the Ptak error estimates, Proceedings of the 9th Annual
Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 8-24**;**** Comm. Appl.
Nonlinear Anal.**, 7, (2000), 2, 87-100.

122. Sufficient convergence conditions for
iteration schemes modeled by point-to-set mappings, Proceedings of the 9th
Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 48-52. ** Appl.
Math. Letters**, Vol. 9, No. 2 (1996), 71-73; Math. Rev. Author index
1996.

123. On the convergence of a
Chebysheff-Halley-type method under Newton-Kantorovich hypotheses,
** Appl. Math. Letters**,
Vol. 6, No. 5 (1993), 71-74; Math. Rev. Author index 1996.

124. On an application of a
variant of the closed graph theorem and the secant method, *Tamkang J. Math***.**, Vol. 24,
No. 3 (1993), 251-267; Math. Rev. 94m:65098, Rabindra Nath Sen.

125. Newton-like methods in
partially ordered Banach spaces, *Approx. Theory Appl***.**, **9**:1
(1993), 1-9; Math. Rev. 94f:47086, Mihai Turinici

126. Results on the Chebyshev
method in Banach spaces, ** Proyecciones Revista**, Vol. 12, No. 2 (1993), 119-128; Math.
Rev. 94j:65078, A.M. Galperin (IL-BGUN; Be'er Sheva).

127. On the convergence of an
Euler-Chebysheff-type method under Newton-Kantorovich hypotheses,
** Pure Math. Appl.**, Vol.
4, No. 3 (1993), 369-373; Math. Rev. 95g:65081, Tetsuro Yamamoto.

128. A note on the Halley
method in Banach spaces, *Appl. Math. Comp***.**, **58**
(1993), 215-224; Math. Rev. 94k:65082, Erich Bohl (Konstanz).

129. On the solution of
underdetermined systems of nonlinear equations in Euclidean spaces, *Pure*** Mathematics and Applications**, Vol. 4, No. 3 (1993), 199-209; Math.
Rev. 95a:65089.

130. On the a posteriori error bounds for
a certain iteration under Zabrejko-Ngyen assumptions, ** Rev. Academia de Ciencias, Zaragoza**,

131. Newton-like methods in
generalized Banach spaces, ** Functiones et Approximatio**,

132. On S-order of
convergence, ** Rev. Academia de Ciencias Zaragoza**,

133. A theorem on perturbed
Newton-like methods in Banach spaces, ** Studia Sci. Math. Hung.**,

134. Some notes on
nonstationary multistep iteration processes, ** Acta Math. Hung.**, Vol. 64, 1 (1994), 59-64; Math.
Rev. 94m:90098.

135. Improved a posteriori
error bounds for Zincenko's iteration, ** Intern. J. Comp. Math**., Vol. 51 (1994), 51-54.

136. The Jarratt method in a
Banach space setting, ** J. Comp. Appl. Math**.,

137. The midpoint method in
Banach spaces and Ptak-error estimates, ** Appl. Math. Comput.**,

138. A convergence theorem for Newton-like
methods under generalized Chen-Yamamoto-type assumptions,
*Appl. Math. Comput**.,
***61**, 1 (1994), 25-37; Math. Rev. 65g:65082.

139. On the convergence of
some projection methods and inexact Newton-like iterations, ** Tamkang J. Math**., Vol. 25, No. 4 (1994), 335-341; Math.
Rev. 95m:65105, Mihai Turinici.

140. On Newton's method and
nonlinear operator equations, *Punj. Univ. J. Math***.**, Vol. 27
(1994), 34-44; Math. Rev. Author index 1996.

141. On the midpoint iterative method for
solving nonlinear operator equations and applications to the solution of integral equations, *Rev. Anal. Numér. Théor. Approx*., Tome **23**, fasc. 2 (1994), 139-152; Math. Rev. 97j:65093.

142. Parameter based algorithms for
approximating local solutions of nonlinear complex equations, ** Proyecciones Math. J.**, Vol. 13,
No. 1 (1994), 53-61; Math. Rev. 95f:65100.

143. The Halley-Werner method
in Banach spaces, *Rev. Anal. Numér. Théor. Approx*., Tome **23**, fasc. 1 (1994), 1-14; Math. Rev. 96c:65099, G. Alefeld
(CD-KLRH-A; Karlsruhe).

144. Error bound
representations of Chebysheff-Halley-type methods in Banach spaces, ** Rev. Academia de Ciencias Zaragoza**,

145. On the discretization of
Newton-like methods, *Inter. J. Computer. Math***.**, Vol. 52
(1994), 161-170.

146. A local convergence
theorem for the super-Halley method in a Banach space, *Appl. Math. Lett***.**, Vol. 7, No. 5 (1994), 49-52; Math.
Rev. Author index 1996.

147. A convergence analysis
for a rational method with a parameter in Banach space, ** Pure Math. Appl.**,

148. On sufficient conditions of the
convergence and an optimality of error estimate for a high speed iterative algorithm for solving nonlinear algebraic
systems, ** Chinese J. Math.**,
Vol. 22, No. 4 (1994), 373-384; Math. Rev. 95i:65078, Xiaojun Chen.

149. On the convergence of
modified contractions, *J. Comput. Appl. Math***.**, **55**,
2 (1994), 183-189; Math. Rev. 96a:65085.

150. A multipoint Jarratt-Newton-type
approximation algorithm for solving nonlinear operator equations in Banach spaces, ** Functiones et Aproximatio Commentarii Matematiki**,

151. Convergence results for
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284. Relaxing convergence conditions of
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287. On a class of nonlinear
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291. Local convergence theorems for
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293. The asymptotic mesh independence
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294. On the approximate
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297. An error analysis for
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302. On a generalization of fixed and
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303. An algorithm for solving
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305. On the monotone convergence of fast
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306. A new semilocal convergence theorem
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308. Error bounds for Newton's
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310. Local and semilocal convergence
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312. On controlling the residuals of some
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314. Enlarging the region of convergence
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317. Local convergence
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318. On the local convergence
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319. A new convergence theorem for the
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322. Relations between forcing sequences
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328. On generalized
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329. On a semilocal
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330. On the convergence of a certain class
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331. Semilocal convergence of
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336. On the radius of
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341. Convergence theorems for Newton-like
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342. Convergence theorems for Newton's
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343. A mesh independence principle for
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344. Relations between
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345. Relations between Newton's method and
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346. The asymptotic mesh independence
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348. Convergence theorems for solving
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350. On the solution of generalized
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351. On the solution of generalized
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354. Approximate solution of linearized
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355. Results on the solution of
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356. On the solution of compact operator
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357. On the solution of
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358. On the convergence of a
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359. A unifying semilocal convergence
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360. On the convergence of
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361. Convergence of Stirling's
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362. A new theorem for
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363. New unifying convergence
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364. Error bounds for Newton's
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365. On the convergence of
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366. Concerning the
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367. Generalized partial
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368. Local convergence
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369. Approximate solution of linearized
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370. A semilocal convergence
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371. New and generalized
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372. On the convergence and application of
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373. On a theorem of L.V. Kantorovich
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374. On the convergence of Newton's method
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375. A unifying theorem on Newton's method
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376. Semilocal convergence for Newton's
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377. On some nonlinear
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378. On the approximation of
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379. Approximating distinct
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380. On a multistep Newton
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381. On the convergence and
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382. A local convergence analysis and
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383. A convergence analysis and
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384. On an application of a fixed point
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385. Generalized conditions for the
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386. An improved error
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387. An improved convergence analysis and
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388. A convergence analysis for Newton's
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389. Concerning the convergence of
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390. A convergence analysis of an
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391. On the convergence and application of
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392. Concerning a local convergence theory
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393. On an improved variant of the L.V.
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394. Concerning the
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395. On the convergence of
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396. Weak sufficient convergence
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397.
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398. On the different convergence radii
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399. Local-semilocal convergence theorems
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400. On the Newton-Kantorovich hypothesis
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401. Concerning the convergence and
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402. On the convergence of a certain class
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403. A convergence analysis and
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404. On the solution and applications of
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405. A mesh independence principle for
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406. A note on a new way of enlarging the
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407. On two improved Durand-Kerner methods
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408. A convergence analysis and
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409. An iterative method for computing
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410. On the comparison of a weak variant
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411. A convergence analysis and
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412. A convergence analysis for a certain
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413. An improved convergence analysis for
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414. On a weak Newton-Kantorovich-type
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415. On a Newton-Kantorovich-type theorem
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416. Some convergence theorems for
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417. On the convergence of Broyden’s
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418. On the convergence of iterates to
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419. Approximating solutions of equations
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420. New sufficient
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421. A convergence analysis for
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422. A semilocal convergence analysis for
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423. On a two-point Newton-like method of
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424.
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426.
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427.
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428.
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429.
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430. On alternative directions to some
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431. On a weak semilocal-local convergence
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432. On the semilocal convergence of the
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433. On the applicability of Newton's
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434. Concerning the convergence of a
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435. An improved approach of obtaining
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436. A semilocal convergence analysis of
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437. Ball convergence theorems for
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438. Lower and upper bounds for the
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439. On the weak Newton method for solving
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440. Enlarging the radius of convergence
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441. On the Newton-Kantorovich method in
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442. On the computation of shadowing
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443. On the semilocal convergence of the
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444. On the computation of continuation
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445. Toward a unified convergence theory
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446. Concerning the “terra
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447. Enlarging the convergence domains of
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448. On a new iterative method of
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449. On
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450. A unified approach for enlarging the
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451. On the approximation of solutions for
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452. A new approach for finding weaker
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453. A convergence analysis and
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454. On the solution of Variational
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455. A semilocal convergence analysis for
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456. A fine convergence analysis for
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457. Relaxing the convergence conditions
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458. A weaker version of the shadowing
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459. A convergence analysis of a
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460. On the convergence of Newton’s
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461. On the secant method for solving non-smooth
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462. On the convergence of fixed slope
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463. Local convergence of the curve
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464. Quasi-Newton methods for solving
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465. Local convergence of Newton’s
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466. On an improved unified convergence
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467. An improved convergence analysis of a
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468. A refined Newton’s mesh
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469. A weaker affine covariant
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470. Convergence of Newton’s method
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471. Local convergence of Newton’s
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472. A unifying local and semilocal
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473. On the solution of variational
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474. Local convergence of Newton’s
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475. On the convergence of Newton’s
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476. A Kantorovich-type analysis for a
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477. On the convergence of the Secant
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478. On the solution of nonlinear
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479. On the convergence of the structured
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480. A non-smooth version of
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481. On a fast two-step method for solving
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482. An improved convergence and
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483. A non-smooth version of
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484. On the solution of variational
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485. On
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486. Weaker conditions for the convergence
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487. An extension of the contraction
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488. On the local convergence of
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489. A note on the solution of a nonlinear
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490. An improved unifying convergence
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491. On the gap between the semilocal
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492. On a quadratically convergent
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493. An improved local convergence
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494. Approximating solutions of equations
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495. An improved convergence analysis for
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496. Newton’s method for variational
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497. On the convergence of the
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498. A refined theorem concering the
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499. A cubically convergent method for
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500. Solving equations using
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501. Concerning the convergence of
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502. A finer mesh independence of
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503. A semilocal convergence analysis for
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504. Improved convergence results for
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505. A Kantorovich analysis of Newton’s
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506. Local convergence of inexact Newton
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507. A weak Kantorovich existence theorem
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508. On the Secant method for solving
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509. Steffensen methods for solving
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510. On a secant –like method for
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511. On the convergence of the midpoint
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512. On the semilocal convergence of a
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513. On the convergence of Newton’s
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514. Local convergence for multistep
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515. On a two step Newton method for
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516. On the radius of convergence of
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517. On the semilocal convergence of a
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518. Approximating solutions of equations
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519. Concerning the radii of convergence
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520. Local convergence of the secant
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521. On the local convergence of a two
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522. On the local convergence of a
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523. An inverse free Newton-Jarratt-type iterative
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524. A comparative study between convergence
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525. Concerning the semilocal convergence
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526. On a quadratically convergent method
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527. On the midpoint method for solving
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528. On the Newton –Kantorovich and
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529. On the semilocal convergence of Newton-like
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530. Multipoint method for generalized equations
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531. Newton’s method in Riemannian
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532. A refined semilocal convergence
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533. A Fréchet –derivative free
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two-step two-point Newton methods for solving nonlinear equations, ** TMPA**,
1, 2, (2013), 47-54.

727. Convergence of Halley’s method
under centered Lipschitz condition on the second derivative, *Rev. Anal. Numér. Théor. Approx**.*, **42**, 1,(2013),3-20.

728. On the Secant method for solving
equations containing nonsmooth operators, ** TMPA**, 1, 7, (2013), 67-77.

729. On the conditioning of semidefinite
programs, ** TMPA**, 1, 5, (2013), 55-62.

730. Newton’s method for solving a
class of optimal design problems, ** TMPA**, 1, 5, (2013), 1-11.

731. Directional secant type methods for
solving equations, ** J. Optim. Th. Appl.**, 157, 2, (2013), 462-485.

732. On a new semilocal convergence
analysis for the Jarratt method, ** J. Ineq. Applic**., 194, (2013).

733. A new convergence analysis for the
two step Newton method of order three. ** Proyecciones J. Math**., 32, 1, (2013),
73-90.

734. Chebyshev-Kurchatov-type methods for
solving equations with non-differentiable operators, ** Transactions on Math. Program and
Applic**., 1, 8, (2013), 17-26.

735. On the computation of fixed points
for random operator equations, ** J. Non. Anal. Opt**., 4, 2, (2013),
105-114.

736. Expanding the applicability of
Newton’s method under Hölder differentiability conditions, ** TMPA**,
1, 4, (2013), 87-97.

737. Extending the applicability of
Newton’s method on Lie groups, ** Appl. Math. Comp**., 219, (2013),
10355-10365.

738. On the convergence of Jarratt method
for solving equations, ** TMPA**, 1, 1, (2013), 41-58.

739. Weaker convergence for Newton’s
method under Hölder differentiability** , Intern. J. Computer. Math**, 91,6,(2014),1351-1369.

740. A unifying semi-local analysis for
iterative algorithms of high convergence order** , J. Non. Anal**.

741. Convergence of Halley’s method
for operators with bounded second Fréchet derivative, ** J. Ineq. Appl.**, 260,
(2013).

742. Improved local convergence analysis
of inexact Gauss-Newton like methods under the majorant condition in Banach
spaces, ** J. Franklin Inst**., (2013).

743. On a bilinear operator free third
order method on Riemannian manifolds, ** Appl. Math. Comput**., 219, (2013),
74229-7444.

744. Expanding the applicability of a
simplified Newton-Tikhonov regularization method for ill-posed problems, ** TMPA**,
1, 4, (2013), 75-85.

745. Expanding the applicability of
Newton-Lavrentiev method for ill-posed problems, ** Boundary Value Problems**,
114, (2013).

746. Expanding the applicability of two
step Newton Lavrentiev method for ill-posed problems, ** J. Non. Anal. Optim**., 4,
2, (2013), 1-15.

747. Inexact Newton methods under weak and
center-weak Lipschitz condition** , Applic. Math**., 10, 2, (2013),
237-258.

748. On an improved convergence analysis
of Newton’s method, ** Appl. Math. Comp**, (2013).

749. Efficient predictor –corrector
Steffensen’s type methods for solving nonlinear equations, ** Transactions
on Mathematical Programing and Applications**, 1, 1, (2013), 41-58.

750. On the secant method,** J.
Complexity**, (2013).

751. Some weaker extensions of the Kantorovich
theorem for solving equations, ** TMPA**, 1, 7, (2013), 57-67.

752. Modification of the Kantorovich-type
conditions for Newton’s method involving twice Frechet differentiable
operators, ** Asian Europ. J. Math**, 6, 3, (2013).

753. An extension of a Theorem by
B.T.Polyak on gradient-type methods, ** Non Funct. Anal. Applic**., 18, 3,
(2013), 411-420.

754. Solving nonlinear equations via an
efficient genetic algorithm with symmetric and harmonious individuals, ** Appl.
Math. Comput**., 219, (2013), 10967-10973.

755. Extending the applicability of
Newton’s method on Riemannian manifolds with values in a cone, ** Asian
Europ. J. Math.,** 6, 3, (2013).

756. Iterative methods for nonlinear
equations or systems and their applications, ** J. Appl. Math**., (2013),
Hindawi Publ. Corp.

757. An improved semilocal convergence
analysis for the Chebyshev method** , J. Appl. Math. Computing**, (2013).

758. On the semilocal convergence of
Stirling’s method based on non-contractive hypotheses, ** TMPA**,
1, 6, (2013), 57-70.

759. A semilocal convergence analysis of
an inexact Newton method using recurrent relations, ** PUJM**, 45,(2013),25-32.

760. On an iterative method of Ulm-type
for solving equations, *Rev. Anal. Numér. Théor. Approx**.**, *

761. On the semi-local convergence of a
two-step Newton-like projection method for ill-posed problems, *Applic.
Math.,40,3,(2013),367-382.*

762. General convergence conditions for m-Fréchet
differentiable operators, ** J. Appl. Math. Computing**.,43,(2013),491-506.

763. Tikhonov’s regularization and a
cubic convergent iterative approximation for non-linear ill-posed problems, ** Advances
and Applications in Mathematical Sciences,(2013)**.

764. Efficient Steffensen-type algorithms
for solving nonlinear equations, *Inter. J. Computer. Math., **90,3,(2013), 691-704.*

765. An intermediate Newton-Kantorovich
method for solving nonlinear equations, **Mathematica**,
(2013).

766. On the method of chord for solving
nonlinear equations, **Mathematica **55,
78, (2013).

767. An improved convergence analysis of
Newton’s method for twice Fréchet differentiable operators, **Applic. Math.**,40,4,(2013),459-481

768. Expanding the applicability of
Lavrentiev regularization methods for ill-posed problems, **Mathematica** 55, 78, (2013).

769. Extended the applicability of
Newton’s method on Riemannian manifolds with values in a cone. **Asian-Europ. J. Math. **6, 3, (2013).

770. An improved semilocal convergence
analysis analysis for a three point method of order 1.839…in Banach
space, **ANVI**, 16, 2, (2013),1-22.

771. Ball convergence for a
Newton-Steffensen-type third order method, **ANVI**,
16, 2, (2013), 1-22.

772. Two-step Newton methods, ** J.
Complexity**, 30, (2014),533-553.

773. Inverse free iterative methods for
nonlinear ill-posed operator equations, **Intern.
J. Math. Sciences**, (2014).

774. On the “terra incognita”
for the Newton-Kantorovich method with applications, ** J. Kor. Math. Soc**.
51,2,(2014),251-266.

775. Newton’s method for
approximating zeros of vector fields on Riemannian manifolds, ** Appl.
Math. Compu**., 762, (2014).

776. Expanding the applicability of
Newton’s method using the Smale alpha theory, ** J. Comput. Appl. Math.**,
261, (2014), 183-200.

777. Newton-type methods on Riemannian
manifolds under Kantorovich type conditions** , Appl. Math. Comput**., 227, (2014),
762-787.

778. A semilocal convergence for a
uniparametric family of efficient secant-like methods** , J. Function Spaces**,
(2014).

779. Convergence of the relaxed
Newton’s method, ** J. Korean Math. Soc., **51, 1, (2014),
137-162.

780. Robust semilocal convergence analysis
for inexact Newton method with relative residual error tolerance, ** Appl.
Math. Comp**., 227, (2014), 741-754.

781. Weaker convergence conditions for the
secant method, ** Applications of Math**. (Chech),(2014).

782. Regularization methods for ill-posed
problems with monotone real part, ** PUJM,46,1,(2014),25-38**.

783. Extending the applicability of
Newton’s method by improving a result due to Dennis and Schnabel, *SeMa
J.,63,1,(2014),63-53*

784. Traub-type high order iterative
procedures on Riemannian manifolds, *SeMA J.,63,1,(2014),27-52.*

785. Expanding the applicability of a two
step Newton-type projection method for
ill-posed problems, ** Functiones et Approximatio**.

786. Relaxed secant-type methods, *Nonlinear
Studies,21,3,(2014),485-503.*

787. Newton-type iterative methods for
nonlinear ill-posed Hammerstein-type
equations, ** Appl. Math**.,41,1,(2014),107-129.

788. On the Newton Kantorovich method for
analytic operators, **ANVI**, 17,
1,(2014),73-82.

789. On the semilocal convergence of
Newton’s method for sections on Riemannian manifolds, *Asian
Europ. J. Math.,7,1,(2014).*

790. On the semilocal convergence of
modified Newton-Tikhonov regularization
method for nonlinear ill-posed problems, *NFFA, **19, 1, (2014), 99-111. .*

791. Convergence analysis for the two step
Newton method of order four, *Rev. Anal. Numér. Théor. Approx**.*, **43**, 1, (2014),
33-44.

792. Expanding
the applicability of Newton-Tikhonov method for ill-posed equations, *Rev. Anal. Numér. Théor. Approx**.*, **43**, 2, (2014),
141-158.

793. On the convergence of Broyden’s
method in Hilbert spaces, **Appl. Math. Comput.
**242, (2014), 945-951.

794. Weak convergence conditions for
Newton-like methods, **TMPA**, 2, 1,
(2014), 13-22.

795. New-w-convergence conditions for the
Newton-Kantorovich method, **PUJM** 46,
1, (2014), 77-86.

796. Semilocal convergence of
Steffensen-type algorithms for solving nonlinear equations, **NFAA **35, (2014), 1476-1499.

797. Expanding the applicability of
Secant-like methods for solving nonlinear equations, **Carpathian Math.J. **(2014).

798. Extending the applicability of
Newton’s method for k-Frechet differentiable operators, **Appl. Math. Comput.** 234, (2014),
167-178.

799. A unified convergence analysis for
secant-type methods, **J. Kor. Math. Soc. **51,
6, (2014), 1155-1175.

800. On the monotone convergence of an
iterative method without derivatives, **TMPA**,
2, 1, (2014), 23-30.

801. Enlarging the convergence domain of
secant-like methods for equations, **Taiwanese
J.Math.** (2014).

802. Iterative regularization for
ill-posed Hammerstein-type operator equations in Hilbert scales, **Stud. Univ.Babes-Bolyai Math. **2,
(2014), 247-262.

803. Expanding the applicability of
Lavrentiev regularization methods for ill-posed
equations under general source condition, **NFAA**,
19, 2, (2014), 177-192.

804. Convergence of Gauss-Newton method
for convex composite optimization II.Applications, **ANVI**, 17, 1, (2014), 61-72.

805. Local convergence analysis of
proximal Gauss-Newton method for penalized least squares problems, **Appl. Math. Comput. **241, (2014),
401-408.

806. Local convergence of the Gauss-Newton
method for injective overdetermined systems under the majorant condition, **J. Kor. Math. Soc. **51, 5, (2014),
955-970.

807. Expanding the applicability of the
Gauss-Newton method for convex optimization under a majorant condition, **SEMA**, 65, 1, (2014), 1-11.

808. Extending the applicability of
Gauss-Newton method for convex optimization on Riemannian manifolds, **Appl. Math. Comput. **249, (2014),
453-467.

809. Fixed point for operators with
generalized Holder derivative, **Asian
Europ. J. Math. **7, 4, (2014),

810. An analysis of the Lavrentiev
regularization methods and Newton-type methods for nonlinear ill-posed
Hammerstein-type equations, **ANVI**,
17, 2, (2014), 26-42.

811. Local convergence of two competing
third order methods in Banach space, **Appl.
Math. **41, 4, (2014), 341-350.

812. Local convergence of
multi-point-parameter of Newton –like methods in Banach space, **NFAA**, 19, 3, (2014), 381-392.

813. Expanding the applicability of the Gauss-Newton
method for convex optimization under a regularity condition, **CANA **21, 2, (2014), 29-44.

814. A convergence analysis of an R-order
method four with reduced computational cost
in Banach spaces, **CANA** 21, 2,
(2014), 1-12 .

815. On an Ulm-like method under weak
convergence conditions in Banach space, **ANVI**,
2, 17, (2014), 1-12.

816. On the local convergence of a
Newton-like method free of bilinear operators, **TMPA** 2, 6, (2014), 13-23.

817. On a damped Newton method for
nonlinear systems, **TMPA**, 2, 6,
(2014), 24-29.

818. On The convergence of the Kurchatov
method under weak conditions, **TMPA**,
2, 6, (2014), 1-12.

819. Iterative methods for nonlinear
equations or systems and their applications 2014, **J. Appl. Math. (Hindawi).**

820. An extension of a theorem by Wang for
Smale’s alpha theory and applications. *Numerical Algorithms, **68, 1,
(2015), 47-60*.

821. Local convergence of deformed Halley
method in Banach space under Holder continuity conditions, **J. Non. Sc. Appl. **(2015), 1-10.

822. Newton’s method on Riemannian
manifolds. **SPR.Book** 2015

823. Ball convergence theorems for fourth
order variants of Newton’s method under weak conditions, **J. Non. Sc. Appl.**(2015).

824. Directional Chebyshev–type
methods for solving equations, *Math. Compu. AMS.*

825. New convergence conditions for the
secant method, *J. Non. Convex. Anal.*

826. Majorizing sequences for
Newton’s method under centered conditions for the derivative, ** Intern.
J. Computer Math**.

827. Expanding the applicability of high
order-Traub-type procedures and their applications, ** JOTA**.

828. An improved convergence analysis for
a two-point Newton method of order three, ** TMPA**.

829. Expanding the applicability of
inexact Newton methods under Smale’s alpha theory, ** AMC**.

830. Weaker Kantorovich-type convergence
criteria for inexact Newton methods, ** J. Compu. Appl. Math**.

831. Expanding the applicability of a
Modified Gauss-Newton method for solving nonlinear ill-posed problems, *Appl.
Math. Comput.*

832. On multipoint iterative processes of
efficiency index higher than Newton’s method*, J. Nonlinear Sci. Appl.*

833. An intermediate Newton iterative
scheme and generalized Zabrejko-Nguen and Kantorovich existence theorems for
nonlinear equations, ** Mathematica**.

834. An improved local convergence analysis
for secant –like method, ** Mathematica**.

835. On the convergence of a derivative
free method using recurrent function, ** J. Appl. Math. Computing**.

836. On a theorem from interval analysis
for solving nonlinear equations, ** Australian J. Math. Anal. Appl.**.

837. On the semilocal convergence of
Newton-like methods using recurrent polynomials, *J. Numer. Anal. Approx. Theory**.*

838. On the convergence region of
Newton’s method under Hölder continuity conditions, ** Intern. J. Computer Mathematics**.

839. On the semilocal convergence of
Newton’s method using majorants and recurrent functions, ** Nonlinear.
Funct. Anal. Appl.**.

840. A comparison between two techniques
for directional cubically convergent Newton methods, *Nonlinear Funct. Anal. Appl.*

841. Unification of sixth order iterative
methods. **Mathematical Sciences.**

842. On the convergence of inexact
Newton-type methods under weak conditions, **J.
Comput. Appl. Math.**

843. A unifying convergence analysis for
Newton’s method and twice Fréchet differentiable operators, **Appl. Math.**

844. The majorant method in the theory of
Newton-Kantorovich approximations and generalized Lipschitz conditions, **J. Comput. Appl. Math.**

845. Expanding the applicability of
Steffensen’s method for finding fixed points of operator equations in
Banach space. **Serrdica Math. J.**

846. Improved local convergence analysis
of Gauss-Newton method under the majorant condition, **Comput. Opt. Appl.**

847. Improved local convergence of inexact
Newton like methods under the majorant condition, **Functiones et Approximatio.**

848. Expanding the applicability of
Tikhonov’s regularization for nonlinear ill-posed problems, **Mathematical Inverse problems.**

849. On the convergence of a damped secant
method with a modified right hand side vector. **Appl. Math. Comput.**

850. Expanding the applicability of the
secant method with applications, **Bull.
Kor. Math. Soc.**

851. Some new developments for
Newton’s method under mild differentiability conditions, **J. Non. Anal. Optim. :Theory and
Applications.**

852. Extending the convergence domain of
Newton’s method for twice Frechet differentiable operators, **Analysis and Applications.**

853. Local convergence for a family of
third order methods in Banach spaces, **PUJM.**

854. A unified local convergence for
Jarratt-type methods in Banach space under weak conditions, **Thai J. Math.**

855. On the convergence of
King-Werner-methods of order 1+sq2 free of derivatives, **Appl. Math. Comput.**

856. On the convergence of an optimal
fourth order family of methods and its dynamics, **Appl. Math. Comput. 252, 336-346.**

857. Local convergence for a family of
multipoint super Halley methods in Banach space under weak conditions, **Appl. Math.**

858. Local convergence for a modified
Halley-like method with less computation
of inversion, **Novi Sad J. Math.**

859. Local convergence of inexact
Gauss-Newton method for singular systems under majorant condition, **SEMA.**

860. Enlarging the convergence ball of the
method of parabola for finding zeros of derivatives, **Appl. Math. Comput.**

__ (J3) Submitted for Publication /Under
Preparation__

861. On the semilocal convergence of
Newton’s method under unifying conditions.

862. On the convergence of Newton-like
methods under general and unifying conditions.

863. On an improved local convergence
analysis for the secant method.

864. Approximation methods for common
solutions of generalized equilibrium problems of nonlinear

865. Note on quadrature based two step
iterative methods for nonlinear equations.

866. A simplified proof of the Kantorovich
theorem for solving equations using scalar telescopic series and related weaker
extensions.

867. A survey on extended convergence
domains for the Newton Kantorovich method.

868. On the semilocal convergence of a
derivative free Chebyshev-Kurchatov three step method for solving equations.

869. Weak convergence conditions for
Newton’s method in Banach space using general majorizing sequences.

870. On the convergence of a double step Secant
method and nondiscrete induction.

871. Efficient three step Newton-like
methods for solving equations

872. Convergence of a Gauss Newton method
for convex composite optimization.

873. Extending the applicability of two
point Newton-like methods under generalized conditions.

874. On the convergence of a Newton-like
method under weak conditions.

875. An improved semilocal convergence
analysis for the midpoint method.

876. An improved semi-local convergence
analysis for the Halley method.

877. On the semilocal convergence of a two
–step Newton-Tikhonov method under weak conditions.

878. Expanding functions through an
iterative integral formulation.

879. Extending the applicability of an
iterative regularized projection method for ill-posed problems.

880. Weak convergence conditions of an
iterative method for solving nonlinear equations.

881. Weaker convergence conditions of
iterated Lavrentiev regularization for nonlinear ill-posed problems.

882. Weak semilocal convergence conditions
for the two step Newton method in Banach space.

883. Enlarging the convergence ball of
Newton’s method on Lie groups.

884. Expanding the applicability of an
aposteriory parameter choice strategy for Tikhonov regularization of nonlinear
ill posed problems.

885. Expanding the convergence domain of
Newton like methods and applications.

886. Discretized Newton-Tikhonov methods
for ill- posed Hammerstein –type equations.

887. Extending the convexity of nonlinear
image of a ball appearing in optimization.

888. Extended convergence of
Newton-Kantorovich method to an approximate zero.

889. The convergence ball of an inexact
Newton-like method in Banach space under weak Lipschitz condition.

890. On the convergence of a Newton-like
method with a modified right hand side vector.

891. Expanding the applicability of the
Gauss-Newton method for a certain class of systems of equations.

892. Local convergence of inexact Newton
like methods under weak Lipschitz conditions.

893. Local convergence of
inexact-Gauss-Newton-like method for least squares problems under weak
Lipschitz condition.

894. On the convergence of a damped
Newton-like method with a modified right hand side vector.

895. Improved error analysis for
Newton’s method for a certain class of operators.

896. Towards optimizing the applicability
of a Theorem by Potra for Newton like methods with applications.

897. On the semilocal convergence of a two
point step Newton method under the gamma condition.

898. Maximum efficiency for a family of
inexact Newton-like methods with frozen derivatives.

899. (=868)?????

900. On a deformed Newton’s method
with third order of convergence under the gamma condition.

901. Expanding the convergence domain for
a family of third order methods.

902. Local convergence for a multi-point
parameter Chebyshev-Halley –type methods of high convergence order.

903. Unified local convergence for
Chebyshev-Halley-type methods under weak conditions.

904. Local convergence of a multi-point family of
high order methods in Banach space under Holder continuous derivative.

905. Iterative regularization methods for
ill-posed Hammerstein –type operator equations in Hilbert scales.

906. On Newton’s method for
subanalytic equations.

907. On the convergence order of efficient
King-Werner –type methods of order 1+sqrt2.

908. 888

909. Local convergence for a family of
three step Newton –type methods

910. 890

911. Local convergence of an at least
sixth order method in Banach spaces.

912. Local convergence of a multipoint
Jarratt-type method in Banach space under weak condition.

913. On a sixth order Jarratt-type method
in Banach spaces.

914. Local convergence of an one parameter
Jarratt-type fourth order method in Banach spaces.

915. Local convergence for a family
of super Halley methods in Banach space
under weak conditions .

916. Local convergence of a uniparametric
Halley-type method in Banach space with free second derivative.

917. Local convergence for a class of
multipoint-super- Halley methods in
Banach spaces under weak conditions.

918. Local convergence for a sixth order
multipoint method in Banach spaces under weak conditions.

919. On the local characterization of some
Newton-like methods of R-order at least three under weak conditions in Banach
space.

920. Extended local convergence for a
family of cubically convergent methods in Banach space.

921. On the local convergence of
secant-like method in a Banach space under weak conditions.

922. Improved convergence analysis of
mixed secant methods for perturbed subanalytic variational inclusions.

923. Local convergence for a family of
sixth order Chebyshev-Halley –type methods in Banach space under weak
conditions.

924. Expanding the applicability of the
secant method under weak and general conditions.

925. Iterative regularization methods for
nonlinear ill-posed operator equations with m-accretive mappings in Banach
space.

926. Local convergence for inverse free
Jarratt—type method in Banach space under Holder conditions.

927. Local convergence of an improved
Jarratt-type method in Banach space.

928. Extending the convergence domain of
the secant and Moser method in Banach space.

929. Improved semilocal convergence analysis for
the secant method in Banach space.

930. Expanding the applicability of the
secant method under weaker conditions in Banach space.

931. Local convergence of a deformed
Jarratt-type method in Banach space without inverses.

932. A unified local convergence analysis of
Newton-like methods.

933. Local convergence of deformed Euler-Halley type
methods in Banach space under weak conditions

934. Local convergence of deformed Chebyshev
method in Banach space under weak conditions.

935. Local convergence of a relaxed
two-step Newton-like method.

936. New semilocal and local convergence
analysis for the secant method.

937. Improved local convergence analysis
for a three point method of convergence 1.839….

938. Improved convergence analysis for
secant –like methods .

939. On an iterative method for
unconstrained optimization .

940. Inexact two point Newton-like methods
in Banach space with applications.

941. Local convergence for a fifth order
method in Banach space.

942. Local convergence and the dynamics of
a two point four parameter Jarratt –like method under weak conditions.

943. A study on the local convergence and
the dynamics of a Chebyshev-Halley –type method free from the second
derivative.

944. Local convergence and the dynamics of
a two- step Newton-like method for equations with simple solution.

945. Local convergence and the dynamics of
a two- step Newton-like method for equations with multiplicity greater than
one.

946. On the local convergence and the
dynamics of a Chebyshev –Halley method with sixth and eighth order of
convergence.

947. Ball convergence theorems and the
dynamics of an iterative method for nonlinear equations.

948. Local convergence and the dynamics of
a sixth order Newton-like method based on Stolarsky and Gini means.

949. Local convergence for some third
order methods under weak conditions.

950. Ball convergence theorems for some
third order iterative methods.

951. Ball convergence theorems for J.
Chen’s one step third order methods.

952. Ball convergence theorems for a fifth
order method in a banch space.

953. Local convergence for a Regula -falsi
–type method under weak conditions.

954. Ball convergence for King’s
fourth order iterative methods.

955. Accessibility of solutions of
operator equations by Newton-like
methods.

956. Cordero later 950.

957. Ball convergence theorems for eighth
order variants of Newton’s method under weak conditions.

958. Ball convergence for three step
Newton loke methods under weak conditions.

959. Ball convergence theorems for
Maheshari –type eighth order methods under weak conditions.

960. Ball convergence results for a method
with memory of efficiency index 1.8392 using only functional values.

961. A study on the local convergence and
the dynamics of a Steffensen –King iterative method.

962. Ball convergence theorems for a
Steffensen-type fourth order method.

963. Ball convergence theorems for a
Steffensen –type third order method.

964. Ball convergence and the dynamics of
some fourth and sixth order iterative methods.

965. Local convergence and the dynamics of
some fifth and sixth order iterative methods.

966. The asymptotic mesh independence
principle of Newton’s method under weaker conditions.

967. Local convergence theorems for some
third order and fourth order methods in Banach space.

968. On the local convergence and the
dynamics of an eighth order method for solving nonlinear equations.

969. Ball convergence theorems for inexact
Newton methods in Banach space.

970. Local convergence for Cauchy-type
method under hypotheses on the first derivative.

971. Ball convergence of second derivative
free Cauchy –type methods under weak conditions.

972. Local convergence of accelerated
Cauchy-type methods.

973. Ball convergence Potra-Ptak
–type Newton methods with optimal third order of convergence.

974. Local convergence of Super-Halley
–type methods with fourth order of convergence under weak conditions.

975. Ball convergence for Hansen-Patrick
–type methods with third and fourth order of convergence under weak
conditions.

976. Ball convergence for a third order
method based on Newton’s method and the Adomian decomposition.

977. Ball convergence of a fifth order
method for solving equations under weak conditions .

978. Ball convergence theorems for general
iterative procedures and their applications.

979. Local convergence of optimal fourth
order methods without memory under hypotheses only up to the first derivative.

980. Ball convergence of a ninth order
method from quadrature and Adomian formulae in Banach space.

981. A unified local convergence for two
step Newton-Like methods with high order of convergence under weak conditions.

982. On the local convergence of
Newton-Like methods with fourth and fifth order of convergence under hypotheses
on the first derivative.

983. A unified local convergence for three
step iterative methods with optimal eighth order of convergence under weak
conditions.

984. Local convergence for a derivative
free iterative method of order there under weak conditions.

__ (K) REPRINT(S) REQUESTS __

The following professors have requested papers:

1.
Etzio Venturino, University of Iowa, (Dept. Math.), USA

2. C.G. Lopez, Madeira, Portugal

3. H. Jarchow, Institute fur Angewandte Mathematik der Universitat Zurich Ch-8001 Zurich, Switzerland.

4. M.S. Khan, King Abdulaziz University, (Dept. Math.), Saudi Arabia

5. Manfred Knebusch, Universitat Regensburg Fakultat fur Mathematik 8400 Regensburg Universitatsstrabe 31, West Germany

6. Ernest J. Eckert, College of Environmental Sciences, The University of Wisconsin-Green Bay, 2420 Nicolet Dr., Green Bay, WI 54302, USA

7. Josef Danes, Mathematical Institute Charles University, Sokolovska 83 18600 Prague 8-Karlin, Chechoslovakia

8. Goral Reddy, Dept. of Mathematics, St. Andrews, Scotland

9. Jerzy Popenda, Dept. of Math., Univesity of Poznan, Poland

10. Vlastimil Ptak, Chechoslovak Academy of Science, Praha, Chechoslovakia

11. Alejandro Figueroa,
Universidad de Magallanes, Punta Arenas-Chile

12. Dragan Jucic, Osijek,
Yugoslavia

13. Ahmad B. Casdam, Multan,
Pakistan

14. Luis Saste Habana, Cuba

15. S.N. Mishra, Lesotho, Africa

16. Josef Kral, Prague,
Checholovakia

17. Juan J. Nieto, Santiago,
Spain

18. S.D. Chatterji, Lausanne,
Switzerland

19. Peter Madhe, Berlin, Germany

20. Ioan Muntean, Cluj, Romania

21. S.L. Singh, Xardwar, India

22. P.D.N. Sriniras, India

23. S. Grzegorskii, Lublin, Poland

24. Toma's Arechaga, Aires, Argentina

25. J.D. Deader, Salt Lake, Utah, USA

26. P. Drouet, Rhone, France

27. J. Weber, The University of Wisconsin, Milwakee, WI, USA

28. David C. Kurtz, Rollins College, USA

29. Jorge L. Quiroz, Colima, Mexico

30. Ming-Po Chen, Taiwan, Republic of China

31. Mustafa Telci, Begtepe, Ankara, Turkey

32. Helmut Dietrich, Merseburg, Germany

33. Dong Chen, Fayeteville, Arkansas, USA

34. Mohammad Tabatabai, Cameron University, OK, USA

35. M.S. Khan, Sultan Quboos University, Muscat, Saltanate of Oman

36. Laszlo Mate, Technical University, Budapest, Hungary

37. H.K. Pathak, Bhilai Nayar, India

38. Osvaldo, Pino Garcia, Havana,
Cuba

39. B.K. Sharma, Ravishankar
University, Raipur, India

40. Aied Al-Knazi, King Abdul Aziz Univ., Jeddah, Saudi Arabia

41. Hassan-Qasin, King Abdul Aziz Univ., Jeddah, Saudi Arabia

42. Tadeusz Jankowski, University Gdansk, Gdansk, Poland

43. K. Kurzak, University Teachers College, Dept. Chemistry, Siedlce, Poland

44. R. Gonzalez, 2000 Rosario, Argentina

45. Emad Fatemi, Ecole
Polytechnique Federale de Lausanne, Switzerland

46. Prasad Balusu, University of Rochester, MI, USA

47. Dieter Schott, Rostolki, Germany

48. J.M. Martinez, IMECC-UNICAMP, Brazil

49. Prasad Balusu, India

50. Qun-sheng Zhou, P.R. China

51. W. Kliesch, Universitat Leipzig, Germany

52. Adriana Kindybalyuk, Ukraine Academy of Sciences, Kiev, Ukraine

53. Roman Brovsek, Ljubljana
Slovenia

54. D. Mathieu, L.M.R.E., France

55. Donald Schaffner, Rutgers University, NJ, USA

56. David Ward, Barron Associates, Charlottesville, VA, USA

57. Eugene Parker, Barron
Associates, Charlottesville, VA, USA

58. Miguel Gomez, Havana, Cuba

59. L. Brueggemann,
Leipzig-Halle, Germany

60. Fidel Delgado, Havana, Cuba

61. B.C. Dhage, Maharashtra,
India

62. Leida Perea, Havana, Cuba

63. David Ruch, Sam Houston University, Huntsville, Texas

64. Patrick J. Van Fleet, Sam Houston University, Huntsville, Texas

65. Tomas Arechaga, BS. Aires,
Argentina

66. M.A. Hernandez, Spain

67. J. Illuateau, Romania

68. Ioan A. Rus, University of Cluj-Napoca, Romania

69. V.K. Jain, Kharagpur, India

70. Alan Lun, University of Melbourne, Victoria, Australia

71. A.M. Saddeek, Assiut University of Mathematics, Assiut, A.R. Egypt

72. Miguel A. Hernandez, Dept. of Mathematics, University de la Rioja, Logrono, Spain

73. James L. Moseley, Dept. of Mathematics, West Virginia University, Morgantown, WV 26500, USA

74. Onesimo Hernandez-Lema,
CINVESTAV-IPN, Dept. of Mathematics, D.F. Mexico

75. R.L.V. Gonzalez, Rosario,
Argentina

76. Jose A. Ezquerro, Logrono,
Spain

77. N. Ramanujam, Bharathidasan
University, Tamil Nadu, India

78. Drouet Pierre, Solaize,
France

79. Michael Goldberg, Las Vegas,
NV, USA

80. Pierre Drouet, Brignai,
France

81. Ravishannar, Shukla, Raipur,
India

82. W. Quapp, Leipzig, Germany

83. Emil Catinas, Cluj-Napoca, Romania

84. Ion Pavaloiu, Cluj-Napoca, Romania

85. Th. Schauze, Lahn, Germany

86. Ioan Lazar, Cluj-Napoca,
Romania

87. Ch. Grossman, Dresden, Germany

88. Livinus, Uko, Medellin, Colombia

89. Z. Athanassov, Bulgarian Academy of Sciences, Sofia, Bulgaria

90. Zhenyu Huang, Nanjing P.R. China

91. John Neuberger, Northern Arizona University, Flagstaff, AZ, USA

92. L.J. Lardy, Syracuse University, Syracuse, NY, USA

93. Kresimir Veselic, Lehrgebiet Mathematische Physik, Hagen, Germany

94. Huang Zhengda, Zhejiang, P.R. China, Columbia University, USA

95.
Vasudeva, Murthy, Bangalore, India

96.
Adeyeye, S. Johnson C. Smith Univ. NC, USA.

97. Narasimham, Andhra, Pradesh, India.

98. Marius Heljiu, Univ.
Petrosani, Hunedoara, Romania.

99. Nicolae Todor, Oncology
institute, Cluj-Napoca, Romania.

100. Pradid Kumar Parida, Kharagpur,
India.

101. Nunchun, China.

102. Proinov, Plovdiv, Bulgaria.

103.Babajee Razin, Univ.
Mauritius, Mauritius.

104.
Dr. Athanasov, Bulgarian Academy of Sciences, Sofia Bulgaria.

105.
Dr. Martin Hermann, Friedrisch –ScHilerr Universitat, Jena, Germany.

106.
H. Haubler.

107.
M. Petkovic.

108.
Benny Neta.

Allesandro
vargas,Prof.Engineering,Brazil,

__(L) ____Seminars__

At the University of Iowa I gave eight seminars per academic year. I continue doing so at New Mexico State and Cameron University ( at an informal basis). During my talks I explain my current work.

__(M) ____Papers
Presented as an Invited Speaker__

1. University of Berkeley, International Summer Institute on Nonlinear Functional Analysis and Applications (1983). Title: "On a contraction theorem and applications".

2. Los Alamos Laboratories (organizers), Conference on Invariant Imbedding, Transport Theory, and Integral Equations, Eldorado Hotel, Santa Fe, NM (1988). Title: "On a class of nonlinear equations arising in neutron transport".

3. Annual Meeting of the American Mathematical Society #863, San Francisco, California, June 16-19, 1991. Title: "On the convergence of algorithmic models" (Chairman of the Numerical Analysis Session (#516), 7:00 p.m. - 9:55 p.m., Thursday, Jan. 17, 1991).

4. Mathematical Association of America, Oklahoma-Arkansas Section, Spring 1991. Title: "Improved bounds for the zeros of polynomials".

5. Annual Meeting of the American Mathematical Society #871, Baltimore, Maryland, Jan. 8-11, 1992. Title: "On the midpoint iterative method for solving nonlinear operator equations in Banach spaces".

6. CAM 92, Edmond, OK, March 27, 1992, University of Central Oklahoma. Title: "On the secant method under weak assumptions".

7. CAM 93, Edmond, OK, February 5, 1993, University of Central Oklahoma. Title: "On a two-point Newton method in Banach spaces of order four and applications".

8. As in (7). Title: "Sufficient convergence conditions for iterations schemes modeled by point-to-set mappings".

9. As in (7). Title: "On a two-point Newton method in Banach spaces and the Ptak error estimates".

10. CAM 94, Edmond, IK, February 4, 1994, University of Central Oklahoma. Title: "On the monotone convergence of fast iterative methods in partially ordered topological spaces".

11. CAM 94, Edmond, OK, February 4, 1994, University of Central Oklahoma. Title: "On a multistep Newton method in Banach spaces and the Ptak error estimates".

12. 56th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 24, 1994. Title: "On an inequality from applied analysis", (Analysis section). It was held at the University of Searcy, Searcy, Arkansas.

13. CAM 95, Edmond, OK, February 10, 1995, University of Central Oklahoma. Title: "A mesh independence principle for nonlinear equations in Banach spaces and their discretizations".

14. 57th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 1995, Southwestern Oklahoma State University, Weatherford, Oklahoma. Title: "On the discretization of Newton-like methods".

15. CAM 96, Edmond, OK, February 9, 1996, University of Central Oklahoma. Title: "A unified approach for constructing fast two-step methods in Banach space and their applications".

16. 58th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 22--23, 1996, Westark Community College, Fort Smith, Arkansas. Title: "Regions containing solutions of nonlinear equations".

17. Second European Congress of Mathematics, International Conference on Approximation and Optimization (ICAOR), Cluj-Napoca, Romania, July 29-August 1, 1996. Title: "On Newton's method".

18. Regional #919 Meeting "Approximation in Mathematics" of the American Mathematical Society in Memphis, TN, University of Memphis, March 21-22, 1997. Title: "Newton methods on Banach spaces with a convergence structure and applications". A.M.S. Abstract #919-65-93.

19. International Conference on Approximation and Optimization, Cluj-Napoca, Romania, May 26-30, 1998. Title: "Relations between forcing sequences and inexact Newton iterates in Banach space".

20. Colloquium Seminars University of Memphis, March 12, 1999. Title: "Recent Developments in Discretization Studies".

21. Research Day Friday, October 27, 2000, University of Central Oklahoma, Edmond, OK. Poster-Talk title: "Developments on the solution of nonlinear operator equations in Banach space and their discretizations".

22. Oklahoma-Arkansas section of the MAA Oklahoma Christian University, March 30, 2001. Talk title: "On the solution of equations on infinite dimensional spaces". President of Section 1E.

23. Oklahoma Academy of Sciences, 90th Annual Technical Meeting, Nov. 2, 2001. Talk and presentation of a paper, Univ. Cameron.

24. Regional Universities Research Day 2001. Poster Presentation, UCO, Edmond, OK, Nov. 9, 2001.

25. 2nd International Conference on Education of the Sciences and Academic Forum, World Coordinating Council of the Science and Academic Forum (SAF). Gave talk, Thessaloniki, Greece, December 7-8, 2001.

26. Regional Universities Research Day 2002. Abstract and Poster Presentation, UCO, Edmond, OK, October 11, 2002.

27. Academic Festival V, March 27-20, 2003 CU. Abstract and Poster Presenter Academic Conference "Beyond Borders: Globalizations and Human Experience".

28.
American Mathematical Society Meeting #988, June 18-21, 2003, Seville, Spain.
Presentation of an abstract and a paper.

29.
Regional Universities Research Day 2003, Nov. 14, abstract and poster
presentation, title: “On Miranda’s Theorem”, UCO, Edmond, OK

30.
ANACM 2004, Chalkis, Greece, September 10-14, 2004, organized session called
“Newton methods”; given talk entitled “Unifying Newton-like
methods”

31.
Research Day 2004, UCO October 29, 2004, abstract and poster presentation,
title: “On the comparison of Moore and Kantorovich theorem in interval
analysis”.

32.Research
day 2005,UCO,November 11,2005,Poster and abstact presentation entitled:On the
Newton-Kantorovich theorem and interior point methods.

33.Participated:”7^{th}
International Conference on Clusters:The HPC Revolution 2006” May 2-4,
2006 OU Norman Oklahoma.

34.Participated
in the Supercomputing conference on October 4,2006,OU Norman Oklahoma.

35.Participated
in the Supercomputing Conference on Clusters:The HPC Revolution 2006,May2-4,2006,Nornan,Ok,,OU(Organ.
Dr. Henry Neeman).

36.Participated
in the Supercomputing Conference
,October 4,2006,Norman ,OK,OU.

37.Research
Day 2006,UCO,December 1,2006,rescheduled for April 6,2007,Poster and abstract
presentation entitled:On an improved convergence analysis of Newton’s
method on Riemannian manifolds.

38.Participated
in the Supercomputing Conference :How to build the fastest super-computer in
USA twice in one academic year.

October
3,2007, Norman OK,OU.

39.Oklahoma
Supercomputing Symposium, October 3,2007:Title:Fastest supercomputer twice in
USA twice in a year ,OU, Norman OK.

40.Research
Day 2007, October 2007, Poster Presentation title: Solving nonlinear equations,
Edmond OK USO.

41.
AMS Annual Meeting, January 6-9,2008,
San Diego California, Invited Speaker, Special Sesssion?Code #SS4A,
Title:Global Optimization

and
Operations Applications Talk title: On the semilocal convergence of
Newton’s Method , Submitted Abstract
Acceptance # 1035-65-357.

42.
International Conference celebrating Popoviciu birthday. Cluj-Napoca Romania
,May 6, 2009,Invited speaker,Title: Finding good starting

points for Newton’s method.

43.Paper
presentation Oklahoma Research day 2009, Broken Arrow Oklahoma (given by
coauthor Ms Zhao)

Title:Enclosing roots of polynomials. A
talk was also given in the Torus conference ,Wichita Falls Texas,February
27,2010.

44.Paper
presentation, Torus Conference, Wichita Falls Texas ,February 27,2010.

45.Poster
Presentation, Oklahoma Research Day 2010, CU, Lawton, OK, November 12,2010.

46.Poster
Presentation,Oklahoma Research Day 2011,
CU, Lawton,OK, Novermber,2011.

47Poster
Presenation,Oklahoma Reasearch Day, 2013, OSU,OK March 8, 2013.

48.
Conference on Numerical Analysis. Gave talk entitled: Unified majorizing
sequences for Traub-type multipoint iterative procedures.

University
of La Rioja, Spain, November 22-23.

49.
Conference on Numerical Analysis: Semilocal convergence of multipoint iterative
methods. University of La Rioja, Spain, November 28-29, 2013.

50.
Poster Presentation with Mr. Akinola, Research Day 2014.

51.Conference
on Numerical Analysis:Semilocal Convergence for multipoint iterative
processes.,University of La Rioja,November 22,2014.

51.CU
Seminar in Mathematics 10-28-14,B026.

52.Poster
Presentation,Oklahoma Research Day 2015 with Mr Akinola.

53.Meeting
1106:Joint Mathematics meeting ,AMS,San Antonio Texas,January 10,2015,

EvenT:Accelerated
advances in multiopbjective optimal control problems and Mathematical
programming based on generalized invexity frameworks.

Invited
speaker:Talk with presentation of a paper.Title:Local convergence for an
improved Jarratt-type method in Banach space.

__(N) ____Selected
Lectures Presented__

1. University of Georgia, 1982-1984

2. University of Iowa, 1984-1986

3. State University of Iowa, 1985

4. Northern University of Viginia, 1986, 1988

5. New Mexico State University, 1986-1990

6. University of Ohio, 1986

7. University of Iowa, 1986, 1988

8. University of New York, 1986-1988

9. University of Texas at El Paso, 1987-1990

10. University of Arizona, I.E.D., 1989, 1990

11. Portland State University, 1990

12. Cameron University, 1990

13. University of Central Oklahoma, 1992, 1993, 1994, 1995, 1996

14.
University of Cyprus, Nicosia Cyprus, 1993,

15.AMS meeting san Antonio Texas,January 10,2015.

__(O) ____Other
Meetings Attended__

1. American Mathematical Society/Mathematical Association of America Annual Meetings, Denver, Colorado, 1983, and Phoenix, Arizona, 1989

2. SIAM Mathematical Meetings, Des Moines, Iowa, 1995

3. International Conference on Theory and Applications of Differential Equations, Ohio University, Athens, Ohio, 1988

4.
Annual Research Conferences of the Bureau of the Census, Arlington, Virginia,
March 21-24, 1993 and 1995.

__5.
TEACHING EXPERIENCE__

*(A)
Courses Taught*

*Graduate
Courses*

1. Real Analysis

2. Functional Analysis

3. Operator Theory

4. Numerical Solutions of Ordinary Differential Equations, Partial Differential Equations, Integral Equations, Integral Differential Equations

5. The Finite Difference and the Finite-Element Method for Ordinary Differential Equations and Partial Differential Equations

6. Differential Equations

7. Partial Differential Equations

8. Special Topics in Functional Analysis, Numerical Functional Analysis, and Differential Equations

9. Numerical Solution of Functional Equations

10. Advanced Numerical Analysis

11. Thesis in Mathematics

12. Optimization

*Undergraduate
Courses*

1. Functional Analysis

2. Real Analysis

3. Numerical Analysis

4. Differential Equations

5. Linear Algebra

6. History of Mathematics

7. Geometry

8. Statistics

9. Abstract Algebra

10. Independent Study in Mathematics

11. Matrix Algebra

12. Survey of Mathematics

13. Intermediate Algebra, regular and computer guided

14. College Algebra, regular and computer guided

15.
Beginning Algebra, regular and computer guided

16.Beginning
and Intermediate Algebra

17.Independent
Study in Mathematics: Undergraduate Research in Nonlinear Programming and
Optimization

18. Calculus 1,2,and 3, and Elementary Calculus

*(B) **Teaching
Effectiveness*

I believe that I have had some success in using computer software for some of the applied Math courses taught in the department. Since my research area is in applied Mathematics it was not difficult for me to use existing software as well as produce my own. It has been desirable for students to use computer software as a facilitating tool in many courses.

I have been attending seminars and conferences as well as constantly reviewing the developments in my field in order to have a broad knowledge of Mathematical subjects. I am trying to be aware of its increasing relevance in our technological age, and be able to stimulate my students to understand and possibly use some of these concepts in their future careers.

I am also concerned with the communication of these ideas to students. Throughout the course I try to make the concepts as understandable as possible by giving examples that help them relate these ideas to topics in that course. I have also provided opportunities to my students in which they can express their views to the class to sharpen their skills in discovering and communicating the concepts. I have used my teaching effectiveness throughout my teaching career.

I
have also produced several textbooks/monographs to be used by students in Mathematics,
Economics, Physics, Engineering, and the applied sciences. Several more on the
same areas have been submitted.

I have reviewed several undergraduate and graduate textbooks (see 4(C)).I reviewed for example the Numerical Analysis textbook entitled "Introduction to Numerical Analysis", by Kendall Atkinson, University of Iowa, published by John Wiley and Sons (1992). The author in his preface recognizes and praises my talents in teaching and expresses his gratitude for my contribution in the improvement of the book. His textbook is considered to be the best book in Numerical Analysis in this country.

I have assisted several students to be accepted in graduate programs at the top universities in this country.

I have also helped them find jobs and still keep in contact with them and their careers after they leave the University.

__6.
AWARDS, HONORS AND AFFILIATIONS__

*(A)
Conference Chairman*

(1) Applied Mathematics Section Annual
Meeting of the American Mathematical Society and Mathematical Association of
America meeting, held at San Francisco, January 1991.

(2) Session organizer conference in
Applied Numerical Analysis and Computational Mathematics,Chalkis,Greece,September
10-14,2004,Session title:Newton Methods.

*(B) **Outstanding
Graduation Record*

I was able to finish both my M.S. and Ph.D. degrees at the University of Georgia at the record time of two years which has not been broken yet.

*(C) **National-International
Recognition*

(1) A total of 98 scientists from five continents have requested reprints of 93% of my published works so far.

(2) I have participated in the evaluation process for tenure and promotion by several U.S. and international universities.

(3) I reviewed several Ph.D. theses of students from the United States and overseas universities.

(4) Nominated for the Distinguished Faculty Award for 1993, 1995, and 2001 Cameron University.

(5) Included in the fourth and consequent editions of "WHO'S WHO AMONG AMERICA'S TEACHERS", 1996. This national organization honors a select 5% of United States teachers.

(6) Received the Distinguished Research award "medal of excellence" by the Southwest Oklahoma Advanced Technology Association, February 23, 2001 (President Bill Burgess, Mezzanine Shepler Center, Cameron University).

(7) Nominated for the Faculty Hall of Fame Award, Cameron University, 2001, 2002, 2003.

(8) Included in the "1000 Great Americans", receiving the medal and plaque by the International Biographical Centre, Cambridge, England.

(9) Received the Lifetime Achievement Award in Mathematics (medal and plaque) (2001) by the International Biographical Centre, Cambridge, England.

(10)Elected Member of the World Coordinating Council of the Science and Academic Forum (SAF) (Nov. 2001) (11 members worldwide, 4 in U.S.). This forum is advising/assisting the Greek government in academic matters.

(11)Nominated for the "Hackler Award for Teaching", Cameron University, Fall 2002.

(12)Included (2002) in the Strathmore's
"Who's Who" and received an award for Mathematical contributions.

(13)Received the Academic Initiative
Award for 2004-2004 (CU#1661).

(14)Received congratulatory letters from
Senators Sam Helton, and Jim Maddox,President Dr. C. Ross, Dean Dr. G. Buckley,
Chairman, Dr. T. Tabatabai.

(15)Elected (2008) to join the
“Round Table Group’s Expert Newtwork” This is one of the
world’s preeminent consortia of consulting experts based in Washington
DC.

(16)Nominated for the CU Research
Award, Spring 2010.

__7.
DEPARTMENTAL SERVICE__

1. Member of the graduate studies committee (N.M.S.U.)

2. Member of the graduate faculty (N.M.S.U.)

3. I have been asked and provided input to the members of the departmental personnel committee concerning hiring, updating the Math majo,the PQIR,the selection of new books and other matters.

4. I have been serving as a regular advisor to students and have helped some of them to present papers and give talks at conferences.

5. Served in the following
committees:Hiring,Personnel,Scholarship,Textbook selection for the classes and
the CU library.

6. Administered the Interscholastic and
CAAPS tests.

7. I coauthored the Interscholastic test
in Geometry (with Dr. Jankovic).

8. I have written a 50 Exercises test
bank to be used as a source for the upper assessment in Mathematics written
test.

9. Wrote letters of reference for 57
students and 17 professors.

10. Browsing Fair Departmental Represenative,August 2006,and April 28,2007,March 2008,2009,March 6,March 27,and November 6,2010, Cameron University.

11. Menber of committees :Screening,scholarship,PQIR,book selection,and other .

__8.
UNIVERSITY SERVICE__

1. I have been participating in the Cameron Interscholastic Service.

2. I have been serving some of the Cameron faculty as consultant.

3. Dean's representative (N.M.S.U.).

4. Southwest Oklahoma Advanced Technology Association
Committee Member(2001-Present)

5. Giving interviews to Lawton
Constitution,Cameron Collegian, KCCU TV,and Wichita magazine.

6. Grievance committee member 2006-2007.

7. CU Academic Fair representative Music
theatre August 2006.

8. Promotion committee (Chair),Screening
Committeee, Scholarship Committee member,2006-2007.

9. President’s Action Commission on Student Retention Committee Member : Fall 2007- 2010.

__9.
COMMUNITY SERVICE__

I have been helping people from Lawton (Fort Sill, Goodyear plant and others) and surrounding areas with their Mathematical problems.

__11. COMPUTING
EXPERIENCE (LANGUAGES)__

(a) Cobol

(b) Fortran

(c) C++

(d) Java

(e) Parallel computing

__12.
CLUB MEMBERSHIP__

(a) American Mathematical Society (since 1982)

(b) Pi Mu Epsilon

(c) MAA until 2002

(d) Upsilon Pi Epsilon

__13.
CITATIONS__

My papers have been cited by other researchers over 1000 times. An internet search for my name produces over 6,200 cites.

__14.
BRIEF DESCRIPTION OF SOME OF THE BOOKS AS LISTED IN 4 (I)__

1.
*The Theory and Applications of Iteration Methods*

This textbook was written for students in engineering, the physical sciences, Mathematics, and economics at an upper division undergraduate or graduate level. Prerequisites for using the text are calculus, linear algebra, elements of functional analysis, and the fundamentals of differential equations. Students with some knowledge of the principles of numerical analysis and optimization will have an advantage, since the general schemes and concepts can be easily followed if particular methods, special cases, are already known. However, such knowledge is not essential in understanding the material of this book.

A large number of problems in applied Mathematics and also in
engineering are solved by finding the solutions of certain equations. For
example, dynamic systems are Mathematically modeled by differences or
differential equations, and their solutions usually represent the states of the
systems. For the sake of simplicity, assume that a time-invariant system is
driven by the equation *x* = *f*(*x*), where *x* is the state.
Then the equilibrium states are determined by solving the equation *f*(*x*)
=0. Similar equations are used in the case of discrete systems. The unknowns of
engineering equations can be functions (difference, differential, and integral
equations), vectors (systems of linear or nonlinear algebraic equations), or
real or complex numbers (single algebraic equations with single unknowns).
Except in special cases, the most commonly used solution methods are iterative
- when starting from one or several initial approximations a sequence is
constructed that converges to a solution of the equation. Iteration methods are
also applied for solving optimization problems. In such cases, the iteration
sequences converge to an optimal solution of the problem at hand. Since all of
these methods have the same recursive structure, they can be introduced and
discussed in a general framework.

In recent years, the study of general iteration schemes has included a substantial effort to identify properties of iteration schemes that will guarantee their convergence in some sense. A number of these results have used an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. In this book, we are concerned with these types of results.

Each chapter contains several new theoretical results and important applications in engineering, in dynamic economic systems, in input-output systems, in the solution of nonlinear and linear differential equations, and in optimization problems.

Chapter 1 gives an outline of general iteration schemes in which the convergence of such schemes is examined. We also show that our conditions are very general: most classical results can be obtained as special cases and, if the conditions are weakened slightly, then our results may not hold. In Chapter 2 the discrete time-scale Liapunov theory is extended to time dependent, higher order, nonlinear differential equations.

In addition, the speed of convergence is estimated in most cases. The monotone convergence to the solution is examined in Chapter 3 and comparison theorems are proved in Chapter 4. It is also shown that our results generalize well-known classical theorems such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the well-known stability theorem of Uzawa. Chapter 5 examines conditions for the convergence of special single-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. The speed of convergence of such methods is examined using the theory of majorants and a method called "continuous induction", which builds on a special variant of Banach's closed graph theorem. Finally, Chapter 6 examines conditions for monotone convergence of special single-step methods such as Newton's method, Newton-like methods, and secant methods generated by point-to-point mappings in a partially ordered space setting.

At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economy.

3. *The Theory and
Application of Abstract Polynomial Equations*

My goal in the text is to present new and important old results about polynomial equations as well as an analysis of general new and efficient iterative methods for their numerical solution in various very general space settings. To achieve this goal we made the text as self-contained as possible by proving all the results in great detail. Exercises have been added at the end of each chapter that complement the material in the sense that most of them can be considered really to be results (theorems, propositions, etc.) that we decided not to include in the main body of each chapter. Several applications of our results are given for the solution of integral as well as differential equations throughout every chapter.

Abstract polynomial equations are evidently systems of algebraic polynomial equations. Polynomial systems can arise directly in applications, or be approximations to equations involving operators having a power series expansion at a certain point. Another source of polynomial systems is the discretization of polynomial equations taking place when a differential or an integral equation is solved. Finite polynomial systems can be obtained by taking a segment of an infinite system, or by other approximation techniques applied to equations in infinite dimensional space.

We have provided material that can be used on the one hand as a required text in the following graduate study areas: Advanced Numerical Analysis, Numerical Functional Analysis, Functional Analysis and Approximation Theory. On the other hand, the text can be recommended for a graduate integral or differential equations course. Moreover, to make the work useful as a reference source, literature citations will be supplied at the end of each chapter with possible extensions of the facts contained here or open problems. We will use graphics and exercises designed to allow students to apply the latest technology. In addition, the text will end with a very updated and comprehensive bibliography in the field. The main prerequisite for the reader is the material covered in: advanced calculus, second course in numerical-functional analysis and a first course in algebra and integral-differential equations. A comprehensive modern presentation of the subject to be described here appears to be needed due to the rapid growth in this field and should benefit not only those working in the field, but also those interested in, or in need of, information about specific results or techniques.

Chapters 1, 2 and 3 cover special cases of nonlinear operator
equations. In particular the solution of polynomial operator equations of
positive integer degree *n* is discussed. The so-called polynomial operators are
a natural generalization of linear operators. Equations in such operators are
the linear space analog of ordinary polynomials in one or several variables
over the fields of real or complex numbers. Such equations encompass a broad
spectrum of applied problems including all linear equations. Often the
polynomial nature of many nonlinear problems goes unrecognized by researchers.
This is most likely due to the fact that unlike polynomials in a single
variable, polynomial operators have received little attention. It must
certainly be mentioned that existence theory is far from complete and what
little is there is confined to local small solutions in neighborhoods which are
often of very small radius. Here an attempt is made to partially fill this
space by doing the following:

(a)
Numerical
methods for approximating distinct solutions of quadratic (*n* =2) (in
Chapters 1 and 2) and polynomial equations (*n* __>__ 2) (in Chapter
3) are given;

(b) Results on global existence theorems not related with contractions are provided;

(c) Moreover for those of a qualitative rather than computational frame of mind, it has been suggested that polynomial operators should carry a Galois theory. In an attempt to inform and contribute in this area we have provided our results at the end of each chapter.

Chapter 4 deals with polynomial integral as well as polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity and other areas. In particular, results on the various Chandrasekhar equations (Nobel Prize of Physics, 1983) are given using Chapters 1-3. These results are demonstrated through the examination of different cases.

In Chapter 5 we study the Weierstrass theorem, Matrix representations, Lagrange and Hermite interpolation, completely continuous multilinear operators, and the bounds of polynomial equations in the following settings: Banach space, Banach algebra and Hilbert space.

Finally in Chapter 6 we provide general methods for solving operator equations. In particular we use inexact Newton-like methods to approximate solutions of nonlinear operator equations in Banach space. We also show how to use these general methods to solve polynomial equations.

6. *A Survey of Efficient
Numerical Methods and Applications*

Our goal in this textbook is to present a survey of new, and important old results about equations as well as an analysis of new and efficient iterative methods for their numerical solution in various space settings. To achieve this goal, we made the textbook as self-contained as possible by providing all the results in great detail. Exercises have been added at the end of each chapter that complement the material. Some of them are results (Theorems, Propositions, etc.) that we decided not to include in the main body of each chapter. Several applications of our results are given for the solution of integral as well as differential equations throughout every chapter.

We have provided material that can be used by undergraduate students at their senior year as well as researchers interested in the following study areas: Advanced Numerical Analysis, Numerical Functional Analysis, Functional Analysis Approximation Theory, Integral and Differential Equations, and all computational areas of Engineering, Economics and Statistics. Moreover, we make the work useful as a reference source, literature citations have been supplied at the end of each chapter with possible extensions of the facts contained here or open problems. The exercises are designed to allow readers to apply the latest technology. In addition, the textbook ends with a very updated and comprehensive bibliography in the field. The main prerequisite for the reader is the material covered in: Advanced Calculus, Advanced Course in Analysis, second course in Numerical-Functional Analysis and a first course in Algebra and Integral-Differential Equations. A comprehensive modern presentation of the Numerical Methods described here appears to be needed due to the rapid growth in this field and should benefit not only those working in the area, but also those interested in, or in need of, information about specific results or techniques.

We use: (E) to denote an equation of the form

*F*(*x*) = 0 (E)

defined on spaces to be specified each time; (N) denotes Newton's method

*x*_*n*+1 = *x*_*n*
- *F*'(*x*_*n*)^-1 *F*(*x*_*n*) (*n* __>__
0), (N)

notation (S) denotes Secant method

*x*_*n*+1 = *x*_*n*
- [*x*_*n*, *x*_*n*-1]^-1 *F*(*x*_*n*) (*n*
__>__ 0) (S)

whereas by [*x*_*n* ,*x*_{*n*-1}] we mean [*x*_*n*
,*x*_{*n* -1};*F*]; and finally (NL) denotes Newton-like method

x_{n +1}= x_n -A(x_n )^{-1} F(x_n ) (n __>__ 0).
(NL)

Chapter 1 serves as an introduction for the rest of the chapters. Topics related with partially ordered topological spaces are covered here. Moreover, divided differences in linear as well as in Banach spaces are being discussed. Furthermore, divided differences, Frechet derivatives, and the relationship between them is being investigated.

Several unpublished results have also been added demonstrating how to select divided differences, Frechet derivatives satisfying Lipschitz conditions or certain new natural monotone estimates similar but not identical to conditions already in the literature of the form, e.g.,

[*x,y*] __<__ [*u,v*]
for *x* __<__ *u* and *y <*

These results are developed, on the one hand because they are needed for the convergence theorems in Chapters 2-4 that follow, and on the other hand because they have an interest of their own.

Chapter 2 deals with the following concern: Applying Newton
methods to solve nonlinear operator equations of the form *F*(*x*)=0
in a Banach space amounts to calculating two scalar constants and one scalar
function over the positive real line. This is due to the fact that conditions
on the Frechet-derivative *F*' of *F* of the form

|| *F*' (*x*) -*F*'(*y*)|| __<__ *L*||*x*
- *y*||, or ||*F*'(*x*) -*F*'(*y*)|| __<__ *K*(*r*)||
*x* - *y*||

or more recently by us ||*F*'(*x* +*h*)-*F*' (*x*)|| __<__
*A*(*r*,||*h*||) for all *x*,*y *in a certain ball
centered at a fixed point *x*_0, of radius *R*>0 with 0 *< r*
__<__ *R* ||*h*|| __<__ *R* - *r* have been
used for the convergence analysis to follow. The constants are of the form *a*
= ||*F*' (*x*_0 )^{-1}|| and *b* = ||*F*'(*x*_0 )^{-1}
*F*(*x*_0)||. The task of computing the constants *L*, *a*,
*b* as well as the functions *K*(*r*) and *A*(*r*,*t*)
is carried out for integral operators *F* in the spaces *X* =*C*,
*L*_p (1 __<__ *p* < infty ) and *L*_\infty.

After going through the first two chapters, we can undertake the main goal discussed in the rest of the text.

Chapter 3 covers the problem of approximating a locally (or
globally) unique solution of the operator equation *F*(*x*)
=0 in the following settings: Banach space, Banach algebra, Hilbert space,
Partially ordered Topological and Euclidean space. In the first four sections,
convergence results are given using Newton (N), Secant (S) as well as
Newton-like methods (NL) under conditions on the divided differences, Frechet
derivatives discussed in the first two chapters. Several results have been
provided to improve upon the ones already in the literature by considering
cases. The following have been done:

(a) Refined proofs using the same techniques are given;

(b) Different techniques have been applied;

(c) New techniques have been used;

(d) New results have been discovered.

In Section 5 the monotone convergence of methods (N), (S) and (NL) is discussed.

Until Section 5, two classes of convergence theorems are discussed: theorems of essentially Kantorovich-type and global theorems based on monotonicity considerations. In Section 5 however a general unifying structure for the convergence analysis which is strong enough to derive both types of theorems from a basic theorem is discussed.

In Sections 6 and 7 results on rates of convergence as well as *Q*- and *R*-orders
are being given respectively. Once recent results of others in this area have
been discussed, we show how to improve upon them.

Chapter 4 deals with the problem discussed already in Chapter 3, but two-step Newton methods are employed as an attempt to improve upon the order of convergence and achieve the highest possible computational efficiency. The flow of Chapter 3 is followed here also. In most cases the superiority of these over single-step methods is being demonstrated.

__15.
BRIEF DESCRIPTION OF PAPERS AS LISTED IN 4 (J)__

The papers concern topics included in the list of research areas listed in 4(J).

The so-called polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many non-linear problems goes unrecognized by researchers. This is most likely due to the fact that unlike polynomials in a single variable, polynomial operators have received little attention. Whether this situation is due to an inherent intractability of these operators or to simple oversight remains to be seen. Hopefully, one should be able to exploit their semi-linear character to wrest more extensive results for these equations than one can obtain in the general non-linear setting.

Examples of equations involving polynomial operators can be found in the literature. My contribution in this area can be found in papers #3, 4, 6-12, 16, 22, 23, 25, 35, 84. Many of the equations of elasticity theory are of this type #3, 4. The problem discussed there pertains to the buckling of a thin shallow spherical shell clamped at the edge and under uniform external pressure.

Some equations in heat transfer, kinetic theory of gases and neutron transport, including the famous S. Chandrasekhar (Nobel in Physics, 1983) integral equation are of quadratic type. Numerical methods for finding small or large solutions of the above equations and their variations as well as results on the number of solutions of the above equations can be found in papers #1-4, 21, 24, 37, 55, 85, 99.

Some pursuit and bending of beams problems can be formulated as polynomial equations. My investigations on such equations can be found in paper #6.

Paper #11 contains results on the study of feedback systems containing an arbitrary finite number of time-varying amplifiers and the study of electromechanical networks containing an arbitrary number of time-varying nonlinear dissipative elements.

Scientists that have worked in this area agree that much work, both of theoretical and computational nature, remains to be done on polynomials in a normed linear space. A summary of some of the remaining problems can be found in my second and third book (see 4(G)).

It must certainly be mentioned that the existence theory is far from complete and what little is there it is confined to local small solutions in neighborhoods which are often of very small radius #1-5, 7-9, 13, 14, 17, 26, 30, 33. In my papers #5, 6, 8, 10, 23, 30, 33, 34, 37, 42, 69, 72, I have provided numerical methods for approximating distinct solutions of polynomial equations under various hypotheses.

As far as I know the above-mentioned authors are the only researchers that have worked on global existence theorems not related with contractions. My contribution in this area is contained in papers #7, 14, 23, 34, 35, 44, 69.

Moreover for those of a qualitative rather than computational frame of mind, it has been suggested that polynomial operators should carry a Galois theory. Such a theory, should it exist, may be very limited, but nonetheless, interesting. The pessimistic note is prompted by the fact that a complete general spectral theory does not exist for polynomial operators. In an attempt to produce such a theory at least the way an analyst understands it, I wrote the relevant papers #18, 23, 34, 35, 45.

The most important iterative procedures for solving nonlinear equations in a Banach space are undoubtedly the so-called Newton-like methods. Indeed, L.V. Kantorovich has given sufficient conditions for the quadratic convergence of Newton's iteration to a locally unique solution of the abstract nonlinear equation in Banach space. His conditions are in some sense the best possible. For the scalar case these conditions coincide with those given earlier by A.I. Ostrowski. Simple sharp apriori estimates were given independently (by different methods) by W.B. Gragg and R.A. Tapia. The method of nondiscrete Mathematical induction was used later by V. Ptak, F. Potra, X. Chen, T. Yamamoto, P. Zabrejko, D. Ngyen, I. Moret et al.; this method yields not only sharp apriori estimates but also convergence proofs through the induction theorem. This method, in which the rate of convergence is now a function and not a number, is closely related with the closed graph theorem. My contribution in this area can be found in the papers 19, 20, 31, 40, 44, 50, 51, 57, 60, 61, 63, 65, 68, 70, 81, 82, 83, 89, 90, 92, 95, 96, 97, 101, 125, 129, 145.

One of the basic assumptions for the use of Newton's method is the condition that the Frechet derivative of the nonlinear operator involved be Frechet-differentiable. There are however interesting differential equations and singular integral equations (see, for example, the work of Etzio Venturino) where the nonlinear operator is only Holder continuous. It turns out that the error analysis of Newton-like methods changes dramatically and the results obtained by the above authors do not hold in this setting. My contribution in this area can be found in the papers #19, 20, 31, 32, 38, 63, 68, 71, 100.

Papers #65, 73, 104, 106 deal with the solutions of nonlinear operator equations containing a nondifferentiable term.

Papers #61, 80, 89, 101, 104, 113 deal with the approximation of implicit functions.

Papers #60, 66, 79, 81, 95, 104 deal with projection methods for the approximate solution of nonlinear equations.

Papers #64, 125, 143 deal with iterative procedures for the solution of nonlinear equations in generalized Banach spaces.

Papers #88, 114, 128, 130, 152 deal with inexact iterative procedures.

Papers #54, 56, 67, 98, 124 deal with the solution of nonlinear operator equations and their discretizations in relation with the mesh-independence principle.

Papers #82, 105, 116 deal with the solution of linear and nonlinear perturbed two-point boundary value problems with left, right and interior boundary layers.

I have applied the above numerical methods, in particular Newton's and its variations to concrete integral equations arising in radiative transfer. See, for example, papers #21, 37. Since the numerical solution of integral equations is closed related to compact operators, I tried in the papers #28, 39, 53, 74 to find some results relating numerical methods and compactness. Work on this subject has already been conducted (see, e.g., the work of P. Anselone and K. Atkinson), but the results so obtained are too general or too particular to be used for my purposes.

Papers #91, 121, 131, 132, 133, 138, 140, 149, 153-218 deal with the convergence and error analysis of multipoint iterative methods in Banach spaces.

Paper #103 deals with the introduction of an optimization algorithm based on the gradient projection technique and the Karmarkar's projective scaling method for linear programming.

Paper #123 (statistics) deals with t-estimates of parameters of general nonlinear models in finite dimensional spaces. The method is highly insensitive to outliers. It can also be applied to solve a system of nonlinear equations.

Papers #62, 74, 76, 93, 94, 107, 134, 139 (Mathematical economics) deal with the convergence of iteration schemes generated by the recursive application of a point-to-set mapping. Our results have been applied to solve dynamic economic as well as input-output systems.

The rest of the papers involve nondifferentiable operator equations on generalized Banach spaces with a convergence structure and inexact Newton methods, as well as iterative procedures using outer or generalized inverses. Globally convergent inexact Newton methods have also been studied. In particular sufficient conditions have been imposed on the residuals in order to achieve the