*CAMERON** UNIVERSITY*

*DEPARTMENT OF MATHEMATICAL SCIENCES*

*LAWTON**, OKLAHOMA
73505-6377, USA*

**CURRICULUM
VITAE**

**IOANNIS KONSTANTINOS
ARGYROS**

**1. PERSONAL**

NAME:

PLACE
OF BIRTH: Athens, Greece.

CITIZENSHIP: USA

ADDRESS:

E-MAIL:

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 secretary)

(580) 536-8754 (Home)

**2. STUDIES**

(1) 1983-1984 Ph.D. in Mathematics,

(2) 1982-1983 M.Sc. in Mathematics,

(3) 1974-1979 B.Sc. in Mathematics,

**3. ACADEMIC EXPERIENCE**

(1) 1994-Present Full Professor,

(2) 1993-1994 Tenured Associate
Professor,

(3) 1990-1993 Associate Professor,

(4) 1986-1990 Assistant Professor,

(5) 1984-1986 Visiting Assistant
Professor,

(6) 1982-1984 Teaching-Research
Assistant,

(7) 1979-1982 Serving the Greek Army,

**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,

(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

*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,

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

29. Communicatons in nonlinear analysis

30. ISRN applied mathematics

31. ANTA,Analyse numerique and
approximation.

__(C) ____Book and Grant Reviewer__

1. *Elementary Numerical Analysis* by Kendall Atkinson,

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 * Vol. 2, ISBN 960-8333-008, 2002,
Evangelos Spandagos. I wrote the Introduction in English, AITHRA Publ.,

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

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

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(

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

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.

__(D) ____Scientific Papers Reviewer__

I have reviewed a total of 435 papers for:

1. *Journal of Computational and Applied
Mathematics*

2. *P.U.J.M.*

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,

11. *Applied Mathematics Letters*

12. *Illinois** Journal of Mathematics*

13. *Korean Journal of Computational and
Applied Mathematics*

14. *Proceeding of the *

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*

*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. **Appled 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*

__(E) ____Grants Received__

1.

2.

3. U.S.A. Army (1988-1990), #DAEA,
26-87-R-0013 (F.M.) Army (jointly with the Mechanical Engineering Department at

4.

5.

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

__(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,

7. Sri Pulak Guhathakurta, Spring 1998,

8. Tariq Iqtadar Khan, Spring 2003,

9. Landlay Khan,Fall 2005,

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

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.

**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,

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:

(b) Promotion-Tenure:

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

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

1. A Contribution to the Theory of
Nonlinear Operator Equations in Banach Space, Master of Science Dissertation,

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,

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,

4. *Dictionary of Comprehensive
Dictionary of Mathematics: Analysis, Calculus and* *Differential
Equations*, (Contributing Author), Editor: Douglas, N. Clark, Chapman-Hall/CRC/Lewis
Publishers,

5. *Computational Methods for Abstract
Polynomial Equations*,

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.,

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.

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,USA2011,ISBN 978-1-61209-522-6.

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

__Books and Monographs Under
Preparation/Accepted__

23. .

__(J1) UNDERGRADUATE RESEARCH__

**(1) **

**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
**

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

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

**Paper Title: Advances on **

**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.**

__(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****: **

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

**Asia: **People's Republic of

**Australia****: **

A 9% of the scientific papers listed below have been published jointly with Professors Mohammad Tabatabai (Cameron, USA), Dong Chen (University of Arkansas, USA), Ferenc Szidarovszky (University of Arizona, USA), Losta Mansor (Libya), Emil Catinas and Ion Pavaloiu (Romania), Ram Verma (Florida, USA), Jose Gutierrez (Spain),M. Hernandez (Spain), J. Ezquerro, (Spain), Huang Zhengda (USA, China), Dr. Uko (USA), Dr. Hilout (France, Morocco), .Dr. R. Ren, Dr. S. Chen (P.R. China)

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.**, Symposium on Nonlinear Functional Analysis and Applications, ** ***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, ** Internat. J. Math. & Math. Sci.**,
Vol. 9, No. 3 (1986), 585--587; Z.F.M.61447044 (1986); Math. Rev. 87j47097,
P.P. Zabrejko (

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 (

5.
Uniqueness-Existence of solutions of polynomial equations in
linear space, ** P.U.J.M.**, 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, ** P.U.J.M.**, 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, ** P.U.J.M.**, 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 (

11.
A note on quadratic equations in Banach space, ** P.U.J.M.**, 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 (

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 (

18.
On *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. et 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, ** P.U.J.M.**,
Vol. XXI (1988), 13-21; Math. Rev. 91g:65136, P.S. Milojevic.

28.
Vietta-Like relations in Banach space, ** Rev. Acad. Ci.
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33.
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34.
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42.
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45.
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51.
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52.
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53.
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54.
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55.
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56.
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57.
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58.
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59.
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61.
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62.
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63.
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64.
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65.
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66.
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67.
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68.
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69.
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70.
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71.
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72.
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73.
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74.
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75.
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76.
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77.
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78.
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79.
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80.
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81.
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82.
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83.
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84.
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85.
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86.
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87.
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88.
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89.
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90.
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91.
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92.
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93.
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95.
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96.
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97.
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98.
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99.
On
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100. Remarks on the convergence of
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101. On the solution of nonlinear operator
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102. On the convergence of
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103. On the convergence of
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104. On some projection methods for the
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105. An initial value method for solving
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106. On the solution of
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107. Some methods for finding error bounds
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108. On the secant method, ** Publicationes Mathematicae Debrecen**, Vol. 43, 3-4 (1993), 223-238; Math.
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109. Improved error bounds for ** Appl. Math. Letters**, Vol. 6, No.
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110. A fourth order iterative
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111. Newton-like methods and
nondiscrete mathematical induction, ** Studia Scientiarum Mathematicarum Hungarica**,

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

113. A mesh independence
principle for nonlinear operator equations in Banach space and their
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114. Sharp error bounds for
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115. An error analysis of
Stirling's method in Banach spaces, *Tamkang J. Math***.,** Vol. 24,
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116. New sufficient conditions for the
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117. On the convergence of
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21, No. 3 (1993), 227-234; Math. Rev. 94f:47088, Mihai Turinici.

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

119. Sufficient conditions for
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120. On a two-point Newton method in
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121. 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
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122. On a two point Newton-method in
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123. Sufficient convergence conditions for
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124. On the convergence of a
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** Appl. Math. Letters**,
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125. 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.

126. Newton-like methods in
partially ordered Banach spaces, *Approx. Theory and Its Applic***.**, **9**:1
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127. 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).

128. On the convergence of an
Euler-Chebysheff-type method under Newton-Kantorovich hypotheses,
** Pure Mathematics and
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129. A note on the Halley
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130. 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.

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

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

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

134. A theorem on perturbed
Newton-like methods in Banach spaces, ** Studia Scientiarum
Mathematicarum Hungarica**,

135. Some notes on
nonstationary multistep iteration processes, ** Acta Mathematica
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136. Improved a posteriori
error bounds for Zincenko's iteration, ** Intern. J. Comp.
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137. The Jarratt method in a
Banach space setting, ** J. Comp. Appl. Math**.,

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

139. A convergence theorem for Newton-like
methods under generalized Chen-Yamamoto-type assumptions,
*Appl. Math. and Comput**.,
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140. 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.

141. On *P.U.J.M***.**, Vol. 27
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142. On the midpoint iterative method for
solving nonlinear operator equations and applications to the solution of integral equations, ** Revue D'Analyse Numerique et de Theorie
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143. Parameter based algorithms for
approximating local solutions of nonlinear complex equations, ** Proyecciones**, Vol. 13, No. 1
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144. The Halley-Werner method in Banach spaces, ** Revue D'Analyse Numerique et de Theorie de l'Approximation**, Tome
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145. Error bound
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146. On the discretization of
Newton-like methods, *Internat. J. Computer. Math***.**, Vol. 52
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147. A local convergence
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148. A convergence analysis
for a rational method with a parameter in Banach space, ** Pure Mathematics and Applications**,

149. 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.

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

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

152. Convergence results for
the super-Halley method using divided differences, *Functiones et Approximatio Commentari Mathematici**, ***XXIII **(1994), 109-122; Math. Rev. 96d:6509.

153. On the aposteriori error
estimates for Stirling's method, ** Studia Scientiarum Mathematicarum Hungarica**,

154. Sufficient conditions for the
convergence of Newton-like methods under weak smoothness assumptions, *Mathematics*, CAM 95, Edmond, OK
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155. On *Tamkang J. Math***.**, Vol. 27,
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156. Stirling's method and
fixed points of nonlinear operator equations in Banach space, ** Bulletin of the Institute of
Mathematics Academic Sinica**, Vol. 23, No. 1 (1995), 13-20; Math. Rev. 96b:65060, A.M.
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157. Error bounds for fast
two-point Newton methods of order four, *Mathematics*, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh
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158. Improved error bounds for
fast two-point Newton methods of order three, *Mathematics*, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh
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159. Stirling's method in
generalized Banach spaces**, ***Annales** Univ.*

160. A unified approach for
constructing fast two-step Newton-like methods, ** Monatshefte fur Mathematik**,

161. On the Secant method and the Ptak error estimates, ** Revue d'Analyse Numerique et de Theorie de l'Approximation**,

162. An error analysis for the secant
method under generalized Zabrejko-Nguen-type assumptions, ** Arabian Journal of Science and Engineering**,

163. Optimal-order parameter
identification in solving nonlinear systems in a Banach space, *Journal of Computational
Mathematics**, ***13**, 3 (1995),
267-280; Math. Rev. 96j:65070, A.A. Fonarev (

164. Nondifferentiable
operator equations on Banach spaces with a convergence structure, ** Pure Mathematics and Applications**, (

165. Perturbed Newton-like methods and
nondifferentiable operator equations on Banach spaces with
a convergence structure, **(S**** WJPAM) Southwest Journal of Pure
and Applied Mathematics**,

166. Results on controlling the residuals
of perturbed Newton-like methods on Banach spaces with a
convergence structure, **(**** SWJPAM) Southwest Journal of Pure
and Applied Mathematics**,

167. A study on the order of convergence
of a rational iteration for solving quadratic equations in a Banach space, ** Rev.
Academia de Ciencias, Zaragoza**,

168. On an application of a variant of the
closed graph theorem to the solution of nonlinear equations, ** Pure Mathematics and Applications**,
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169. Results on ** Appl. Math. and Comp.**,

170. Results on ** Appl. Math. and Comp.**,

171. On the method of tangent
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172. A unified approach for constructing
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173. On the method of tangent
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174. On an extension of the
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175. An inverse-free Jarratt
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176. An error analysis for the Steffensen
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177. Concerning the convergence of inexact
Newton-like methods on Banach spaces with a convergence structure and
applications, Proceedings of the International Conference on Approximation and
Optimization (Romania) **- ICAOR
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178. Improved error bounds for
an Euler-Chebysheff-type method, ** Pure Math. Appl.** (

179. On the convergence of perturbed
Newton-like methods in Banach space and applications, ** Southwest J. Pure Appl. Math.**,

180. Sufficient conditions for the
convergence of iterations to points of attraction in Banach spaces, ** Southwest J. Pure Appl. Math.**,

181. Weak conditions for the
convergence of iterations to solutions of equations on partially ordered
topological spaces**, ***Southwest J. Pure Appl. Math***.**, **2**
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182. On the monotone
convergence of implicit Newton-like methods, *Southwest J. Pure
Appl. Math***.**, **2** (1996), 55-59; Math Rev. 98b:65063.

183. A generalization of
Edelstein's theorem on fixed points and applications, *Southwest J. Pure Appl. Math***.**, **2**
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184. Generalized conditions
for the convergence of inexact Newton methods on Banach spaces with a
convergence structure and applications, ** Pure Mathematics and
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185. Error bounds for an
almost fourth order method under generalized conditions, *Rev. Academia de Ciencias***, Zaragoza**,

186. A simplified proof concerning the
convergence and error bound for a rational cubic method in Banach spaces and applications to nonlinear integral
equations, ** Rev. Academia de
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187. On the convergence of
Chebysheff-Halley-type method using divided differences of order one, ** Rev. Academia de Ciencias, **,

188. On the convergence of
two-step methods generated by point-to-point operators, *Appl. Math. and Comput***.**, **82**, 1 (1997), 85-96; Math.
Rev. 97m:65107, A.M. Galperin, Boro Doring.

189. Improved error bounds for
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190. Inexact ** Approx. Th. Applic.**,

191. A mesh independence
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413. A convergence analysis for a certain
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Inequalities**, ***7**, 1 (2004), 133-142.

414. An improved convergence analysis for
the secant method based on a certain type of recurrence relations**, Intern.
J. Comput. Math.**,

415. On a weak Newton-Kantorovich-type
theorem for solving nonlinear equations in Banach space, *Advances in Nonlinear Variational Inequalities**, ***7**,
2 (2004), 101-109.

416. On a Newton-Kantorovich-type theorem
for solving equations in a Banach space and applications, *Advances in Nonlinear Variational Inequalities**, ***7**,
2 (2004), 79-88.

417. Some convergence theorems for ** Pan
American Mathematical Journal**,

418. On the convergence of Broyden’s
method, ** Communications on Applied Nonlinear Analysis**,

419. On the convergence of iterates to
fixed points of analytic operators, **Revue
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420. Approximating solutions of equations
using two-point methods, **Appl. Num. Anal.
Comp. Math.**,1, 3, (2004), 386-412.

421. New sufficient
convergence conditions for the secant method, *Chechoslovak
Mathematical Journal**, 55, 130, (2005), 175-187.*

422. A convergence analysis for
Newton-like methods for singular equations using outer or generalized inverses,
*Applicationes
Mathematicae**, 32, 1, (2005), 37-49.*.

423. A semilocal convergence analysis for
the method of tangent parabolas, *Rev. Anal. Numer. Theor. Approx.**, 34, 1, (2005), 3-15.*

424. On a two-point Newton-like method of
convergence order two, *Int. J. Computer Math.**, 88, 2, (2005), 219-234.*

425.
Convergence
radii for *Pan American* *Mathematical Journal**, 15, 1, (2005), 12-28.*

426.
Convergence
radii for *Pan American* *Mathematical Journal**, 15, 1, (2005), 41-46.*

427.
On the convergence of *Communications
in Applied Nonlinear**, 12, 1, (2005), 51-58.*

428.
On the semilocal convergence of *Advances in
Nonlinear Variational Inequalities**, 8, 1, (2005)71-82.*

429.
On some theorems concerning the
convergence of ** Advances in Nonlinear Variational
Inequalities**,

*430. *A
semilocal convergence analysis for a deformed *Mathematical Sciences Research Journal**, 9, 8, (2005), 217-222.*

431. On alternative directions to some
theorems of Smale and Rheinboldt concerning Newton-like method, **Advances in Nonlinear Variational
Inequalities**, 8, 1, (2005), 57-62.

432. On a weak semilocal-local convergence
theorem for **Advances in
Nonlinear Variational Inequlaities**, 8, 1, (2005), 103-110.

433. On the semilocal convergence of the
secant method under relaxed conditions, **Advances
in Nonlinear Variational Inequalities**, 8, 1, (2005), 119-132.

434. On the applicability of Newton's
method for solving equations in a Banach space under center-Lipschitz-type
conditions, **Advances in Nonlinear Variational
Inequalities**, 8, 1, (2005), 1313-142.

435. Concerning the convergence of a
certain class of Newton-like methods in a Banach space, **Advances in Nonlinear Variational Inequalities**, 8, 1, (2005), 143-153.

436. An improved approach of obtaining
good starting points for solving equations by Newton's method, **Advances in Nonlinear Variational
Inequalities**, 8, 1, (2005), 111-118.

437. A semilocal convergence analysis of **Advances
in Nonlinear Variational Inequalities**, 8, 2, (2005), 53-59.

438. Ball convergence theorems for **Advances
in Nonlinear Variational Inequalities**, 8, 2, (2005), 61-68.

439. Lower and upper bounds for the
distance of a manifold to a nearby point, **Advances
in Nonlinear Variational Inequalities**, 8, 2, (2005), 69-73.

440. On the weak Newton method for solving
equations in a Banach space, **Advances in
Nonlinear Variational Inequalities**, 8, 2, (2005), 49-52.

441. Enlarging the radius of convergence
for iterative methods by using a one parameter operator imbedding, **Advances in Nonlinear Variational
Inequalities**, 8, 2, (2005), 75-80.

442. On the Newton-Kantorovich method in
Riemannian manifolds, **Advances in
Nonlinear Variational Inequalities**, 8, 2, (2005), 81-85..

443. On the computation of shadowing
orbits for dynamical systems, **Advances
in Nonlinear Variational Inequalities**, 8, 2, (2005), 87-91.

444. On the semilocal convergence of the
Gauss-Newton method, **Advances in
Nonlinear Variational Inequalities**, 8, 2, (2005), 91-93.

445. On the computation of continuation
curves for solving nonlinear equations, **Advances
in Nonlinear Variational Inequalities**, 8, 2, (2005), 101-108.

446. Toward a unified convergence theory
for **Advances in Nonlinear Variational Inequalities**, 8, 2, (2005), 109-120.

447. Concerning the “terra
incognita” between convergence regions of two **Nonlinear Analysis**, 62, (2005), 179-194.

448. Enlarging the convergence domains of **Advances
in Nonlinear variational Inequalities**, 8, 2, (2005), 121-129.

449. On a new iterative method of
asymptotic order 1+√2 for the computation of fixed points, **Intern. J.Computer Mathematics**, 82, 11, (2005), 1413-1428.

450. On
an application of a weak Newton-Kantorovich theorem to nonlinear finite
element analysis, **Mathem. Sciences Research
Journal**, 9,12, (2005), 330-337.

451. A unified approach for enlarging the
radius of convergence for **Nonlinear
Functional Analysis and Applications**, 10, 4, (2005), 555-563.

452. On the approximation of solutions for
generalized equations , **Communications
in Applied Nonlinear Analysis**, 12,2,(2005),97-107.

453. A new approach for finding weaker
conditions for the convergence of **Applicationes Mathematicae**,
32, 4, (2005), 465-475.

454. A convergence analysis and
applications of two-point Newton-Like methods in Banach space under relaxed
conditions, **Aequationes Mathematicae**,
70, (2006), 124-148.

455. On the solution of Variational
Inequalities under weak Lipschitz conditions, **Advances in Nonlinear Variational Inequalities**, 9, 1, (2006), 85-94.

456. A semilocal convergence analysis for
Newton LP methods, **Advances in Nonlinear
Variational Inequalities**, 9, 1, (2006), 75-84.

457. A fine convergence analysis for
inexact **Functiones et Approximatio
Commentari Mathematici**, XXXVI, (2006),7-31.

458. Relaxing the convergence conditions
for Newton-like methods, **J.Appl. Math.
And Computing**, 21, 1-2, (2006), 119-126.

459. A weaker version of the shadowing
lemma for operators with chaotic behavior, ,**Intern. J. Pure and Appl. Math.**, 28, 3, (2006), 417-422.

460. A convergence analysis of a Newton-like
method without inverses., Int. **J. Pure
and Appl. Math.**, 30, 2, (2006), 143-149.

461. On the convergence of **Nonlinear
Funct. Anal. And Appl.**,11, 2, (2006), 201-214.

462. On the secant method for solving non-smooth
equations, **J. Math. Anal. Appl.**, 322,
1, (2006), 146-157, MR2238155 65H10, (47125,90C56).

463. On the convergence of fixed slope
iteartions, **PUJM**, 38, (2006), 39-44.

464. Local convergence of the curve
tracing for the homotopy method, **Revista
Colombiana des Matematicas**, 40, (2006), 417-422.

465. Quasi-Newton methods for solving
generalized equations, **Nonlinear
Functional Analysis and Applications**, 11, 4, (2006), 647-654.

466. Local convergence of **J. Korean Soc. Math.
Educ. Ser. B. Pure and Applied Math.**, 13,4, (2006), 261-267.

467. On an improved unified convergence
analysis for a certain class of Euler-Halley-type methods, **J. Korean Soc. Math. Educ.Ser.B.**,13,3, (2006), 207-216.

468. An improved convergence analysis of a
super quadratic method for solving equations, **Revista Colombiana des Matematicas**, 40,1,(2006),65-73.

469. A refined **Central European J. Math.**, 4, 4, (2006), 562-572.

470. A weaker affine covariant
Newton-Mysovskikh theorem for solving equations, **Applicationes Mathematicae**, 33,3-4, (2006), 355-363.

471. Convergence of **Proyecciones,Iniversidad
Catolica De Norte**, 25, 3, (2006), 293-306.

472. Local convergence of **Punjab University Journal of
Mathematics (PUJM)**, 38, (2006), 1-7.

473. A unifying local and semilocal
convergence analysis of Newton-like methods, **Advances in Nonlinear Variational Inequlities**, 10,1,(2007),1-12.

474. On the solution of variational
inequalities on finite dimensional spaces, **Advances
in Nonlinear Variational Inequalities**,10,(1,(2007),69-77.

475. Local convergence of **Advances in Nonlinear Variational
Inequalities**, 10, 1, (2007), 101-111.

476. On the convergence of **J.
Comput. Appl. Math.**, 205, (2007), 584-593.

477. A Kantorovich-type analysis for a
fast iterative method for solving nonlinear equations, **J. Mathem. Anal. Applic., **332,
(2007), 97-108.

478. On the convergence of the Secant
method under the gamma condition**,
Central European Journal of mathematics**, 5, 2, (2007), 205-214.

479. On the solution of nonlinear complementarity
problems, **Advances in Nonlinear
Variational Inequalities**, 10, 1, (2007), 79-88.

480. On the convergence of the structured
PSB update in Hilbert space, **International
Journal of Pure and Applied Mathematics**, 34, 4, (2007), 519-524.

481. A non-smooth version of
Newton’s method using Locally Lipschitzian operators, **Rendiconti Circolo Matematico Di Palermo**,
56, (2007), Ser.II,Tomo, LVI, (2007), 5-16.

482. On a fast two-step method for solving
nonlinear equations, **International
Journal of Pure and Applied Mathematics**, 34, 3, (2007), 313-321.

483. An improved convergence and
complexity analysis of Newton’s method for solving equations, **International Journal of Computer Mathematics**, 84, 1, (2007), 67-73.

484. A non-smooth version of **International
Journal of Computer Mathematics**, 84, 12, (2007), 1747-1756.

485. On the solution of variational
inequalities on finite dimensional spaces, **Advances
in Nonlinear Variational Inequalities**, 10, 1, (2007), 69-77.

486. On
the convergence of Broyden-like methods, **Acta Mathematica Sinica,English Series**, 23, 6, (2007), 965-972

487. Weaker conditions for the convergence
of Newton-line methods, **Revue
D’Analyse Numer. Theor. Approx.,** 36, 1, (2007), 39-49.

488. An extension of the contraction
mapping principle, **J. Korean Soc. Math.
Ed.Ser. B.Pure and Appl. Math.**,14,4,(2007),283-287.

489. On the local convergence of **Pan American Math.**, J.17,4,(2007),101-109.

490. A note on the solution of a nonlinear
singular equation with a shift in a generalized Banach space, **Journal **, 14, 4,
(2007), 279-282.

491. An improved unifying convergence
analysis of **J. Appl.
Math. And Computing**, 25, 1-2, (2007),

492. On the gap between the semilocal
convergence domain of two **Applicationes Mathematicae**,
34, 2, (2007), 193-204.

493. On a quadratically convergent
iterative method using divided differences of order one, **J. Korea S. M. E. Ser. B.**, 14, 3, (2007), 203-221.

494. An improved local convergence
analysis for secant-like methods, **East
Asian Math.** **J.**, 23, 2, (2007), 261-270.

495. Approximating solutions of equations
using **Revue D’Analyse
Numer. et de Th. Approx.,** 36, 2, (2007), 123-137.

496. An improved convergence analysis for
the secant method under the gamma condition, **PUJM, **39, (2007), 1-11.

497. **Applicationes Mathematicae**, 34, 3, (2007), 349-357.

498. On the convergence of the
Newton-Kantorovich method:The generalized Holder case**. Nonlinear studies**, 14, 4, (2007), 355-364.

499. A refined theorem concering the
conditioning of semidefinite programs, **J.
Appl. Math. and Computing**., 24(1-2), (2007), 305-312.

500. A cubically convergent method for
solving generalized equations without second order derivatives, **Intern J. Modern Math**, 3, 2, (2008), 187-196.

501. Solving equations using **Revue D’Anal. Numer. Th.
Approx.**, 37, 1, (2008), 17-26.

502. Concerning the convergence of **Nonlinear
Functional Analysis and Application**, 13, 1, (2008), 43-59.

503. A finer mesh independence of **Nonlinear Functional Analysis and
Application**, 13, 3, (2008), 357-365.

504. A semilocal convergence analysis for
a certain class of modified **East Asian J. Math.**, 24, 2,
(2008), 151-160.

505. Improved convergence results for
generalized equations**, East Asian Math.
J.**, 24, 2, (2008), 161-168.

506. A Kantorovich analysis of **, J. Concrete and Applicable
Anal.**, 6, 1, (2008), 21-32.

507. Local convergence of inexact **Intern J. Modern
Mathem.**, 3, 1, (2008), 11-19.

508. A weak Kantorovich existence theorem
for the solution of nonlinear equations**,
J. Math. Anal. Appl.**, 342, (2008), 909-914.

509. On the Secant method for solving
nosmooth equations and nondiscrete induction, **Nonlinear Functional Analysis and
Applications**, 13, 1, (2008), 147-158.

510. Steffensen methods for solving
generalized equations, **Serdica Mathem.
J.,** 34, (2008), 1001-1012.

511. On a secant –like method for
solving generalized equations, **Mathematica
Bohemica**, 133, 3, (2008), 313-320.

512. On the convergence of the midpoint
method, **Numerical Algorithms**, 47, (2008),
157-167.

513. On the semilocal convergence of a
Newton-type method in Banach spaces under the gamma-condition, **J. Concrete and Appl. Anal.**, 6, 1, (2008),
33-44.

514. On the convergence of **J. Korea
Math. Soc. Math. Educ. Ser. B: Pura and Appl. Math**., 15, 2, (2008), 111-120.

515. Local convergence for multistep
simplified Newton-like methods**, PUJM**,
40, (2008), 1-7.

516. On a two step **Commun. on
Applied Nonlin. Anal.**, 15, 1, (2008), 85-93.

517. On the radius of convergence of **Nonlinear Functional Analysis and Applications**, 13, 3, (2008), 409-415.

518. On the semilocal convergence of a
fast two step method, **Revista Colombiana
de Matematicas**, 42, 1, (2008), 1-10.

519. Approximating solutions of equations
by combining **. Korea Math. Soc. Educ. Ser.
B: Pure and Appl.Math**., 15, 1, (2008), 35-45.

520. Concerning the radii of convergence
for a certain class of Newton-like methods. **J. Korea Math. Soc. Educ. Ser. B: Pure and Appl.Math.**, 15, 1, (2008),
47-55.

521. Local convergence of the secant
method under Holder continuous divided differences, **East Asian J. Math.**, 24, 1, (2008), 21-26.

522. On the local convergence of a two
step Steffensen-type method for solving generalized equations, **Proyecciones**, 27, 3, (2008), 319-330.

523. On the local convergence of a
Newton-type method in Banach space under the gamma condition, **Proyecciones**, 27, 1, (2008), 1-14.

524. An inverse free Newton-Jarratt-type iterative
method for solving equations, **J. Appl. Math.
Computing**, 1-2, 28, (2008), 15-28.

525. A comparative study between convergence
theorems for **J. Korea Math. Soc. Educ. Ser. B:
Pure and Appl. Math.**, 15, 4, (2008), 365-375.

526. Concerning the semilocal convergence
of **Rendiconti
Circolo Matematico di Palermo**, 57, (2008), 331-341.

527. On a quadratically convergent method
using divided differences of order one under the gamma condition, **Central European J. Math., **6, 2, (2008),
262-271.

528. On the midpoint method for solving
generalized equations, **PUJM**, 40, (2008),
63-70.

529. On the Newton –Kantorovich and
Miranda theorems**, East Asian J. Math**.,
24, 3, (2008), 289-293.

530. On the semilocal convergence of
Newton-like methods for solving equations containing a nondifferentiable term, **East Asian J.Math.**, 24, 3, (2008), 295-304.

531. Multipoint method for generalized equations
under mild differentiability conditions,Functiones et Approximation, **Comentarii Matematici**, 38, 1, (2008), 7-19.

532.
Newton’s method in Riemannian
manifolds, **Revue D’Analyse
Numérique et de Théorie D’ Approximation**, 37, 2, 1, (2008), 119-125.

533. A refined semilocal convergence
analysis of an algorithms for solving the Ricatti equation, **J. Appl. Math. Computing**., 27(1-2),
(2008), 339-344.

534. A Fréchet –derivative free
cubically convergence method for set valued maps**, Numerical Algorithms**, 4, 48, (2008), 361-371.

535. A cubically convergent method for
solving generalized equations**. Inter. J.
Modern Math., **3(2),
(2008), 187-195.

536. Local convergence analysis for a
certain class of inexact methods, **The
Journal of Nonlinear Sciences and its Applications**, 2, 1, (2009), 11-18.

537. On the comparison of a
Kantorovich-type and Moore Theorems, **J.
Appl. Math. and Computing**, 29, (2009), 117-123.

538. Concerning the convergence of **J. Appl. Math. and
Computing**, 29, (2009), 391-400.

539. **J. Appl. Math. and Computing**, 29, (2009), 417-427.

540. On the convergence of inexact
Newton-type methods using recurrent functions, **Pan American Math. J**., 19, 1, (2009), 79-96.

541. Local convergence of inexact
Newton-like methods, **The Journal of Nonlinear
Sciences and its Applications**, 2(1),
(2009), 11--18.

542. Local convergence results for **J. Korea Math. Soc. Educ. Ser. B: Pure and
Appl. Math.**, 16, 1, (2009).

543. An improved Newton-Kantorovich
theorem and interior point methods**, East
Asian J. Math.**, 25, 2, (2009), 147-151.

544. Convergence of the **East Asian J. Math.**, 25, 2, (2009), 153-157.

545. Local convergence of Newton-like
methods for generalized equations, **East
Asian J. Math.**, 25, 4, (2009), 425-431.

546. On the semilocal convergence of
inexact **, J. Comput.
Appl. Math.**, 228, 1, (2009), 434-443.

547. A convergence analysis of **Applicationes Mathematicae**, 36, 2, (2009), 225-239.

548. On **J. Appl. Math. Computing**,
31,(1-2), (2009),97-111.

549. On **Numerical Algorithms**,
52, (2009), 295-320.

550. On a class of Newton-like methods for
solving nonlinear equations, **J. Comput. Appl.
Math.**, 228, (2009), 115-122.

551. A generalized Kantorovich theorem on
the solvability of nonlinear equations, **Aequationes
Mathematicae**, 77, (2009), 99-105.

552. An improved mesh independence
principle for solving equations and their discretizations using Newton’s
method, **Australian J. Mathematical
Analysis and Applications**, 6, 2, 2, (2009), 1-11.

553. Finding good starting points for
solving equations by Newton’s method, **Revue D’Analyse Numerique et de Theorie de l’Approximation**,
39, 1, (2010), 3-10.

554. On the Newton Kantorovich theorem and
nonlinear finite element methods**, Applicationes
Mathematicae**, 36, 1, (2009), 75-81.

555. **, J. Appl. Math. Computing**, 31,(1-2), (2009),
217-228.

556. On local convergence of a Newton-type
method in Banach spaces, **Intern. J.
Computer Math., **86(8), (2009), 1366-1374.

557. On an improved local convergence
analysis for the Secant method, **Numerical
Algorithms**, 52, (2009), 257-271.

558. Semilocal convergence of **ANVI**,
13, 1, (2009), 65-73.

559. Convergence analysis for
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Functional Analysis and Applications**, 1, (2010), 21-32, Nova science Publ.Inc.

560. On the local convergence of the
midpoint method in Banach spaces under the gamma- condition, **Proyecciones J. Math**., 28, 2, (2009),
155-167.

561. On the convergence of a modified **PUJM**, 41, (2009), 11-21.

562. On the convergence of Steffensen’s
method on Banach spaces under the gamma-condition, **Communications on Applied Nonlinear Analysis**, 16, 4, (2009), 73-84.

563. A new semilocal convergence theorem
for **Atti
Semin. Fis. Univ. **, 56, (2008-2009), 31-40.

564. An improved local convergence
analysis for a two-step-Steffensen-type method, **J. Appl. Math. Computing**, 30, (2009), 237-245.

565. Generalized equation, variational
inequalities and a weak Kantorovich theorem, **Numer. **,
52, (2009), 321-333.

566. Convergence theorems for **J. Kor. Soc. Math. Ser. B. Pure and Applied Math**., 16, 4, (2009).

567. An improved convergence analysis of **Mathematica**, 51, 74, 2, (2009), 1-14.

568. On the convergence of the modified
Newton’s method under Holder continuous Fréchet-derivative,**
Appl. Math. Comput.**, 213, (2009), 440-448.

569. On the convergence of modified **J. Comput. Appl. Math.**, 231(2), (2009), 897-906.

570. On the convergence of a Jarratt-type
method using recurrent functions. **J.
Pure and Appl. Math.: Advances and Applications**, 2(2), (2009), 121-144.

571. On multipoint iterative processes of
efficiency index higher than **J. Nonlinear science Appl., **2,
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572. On the implicit iterative processes
for strictly pseudocontractive mappings in Banach spaces, **J. Comput. Appl. Math.**, 233, 2,(2009), 208-216.

573. Enclosing roots of polynomial
equations and their applications to iterative processes, **Surveys in Mathematics and its Applications**, 4, (2009), 119-132.

574. On the convergence of Newton-type
methods under mild differentiability conditions, **Numerical Algorithms**, 52, 4, (2009), 701-726.

575. On the convergence of some iterative
procedures under regular smoothness, **Pan.
Amer. Math. J.**, 19, 2, (2009), 17-34.

576. On the convergence of two step
Newton-type methods of high efficiency index, **Applicationes Mathematicae**, 36, 4, (2009), 465-499.

577. On the convergence of Stirling’s method in Banach spaces
under gamma-type condition, **ANVI**,
12, 2, (2009), 17-23.

578. On the convergence of **J.**
**Korean Soc. Math. Educ. Ser. B Pure and
Applied math.**, 16, 1, (2009), 13-18.

579. On the local convergence of the
Gauss-Newton method, **PUJM**, 41,
(2009), 23-33.

580. An improved local convergence
analysis for Newton-Steffensen-type methods, **J. Appl. Math. and Computing**, 32, (2010), 111-118.

581. Inexact **Nonlinear
Functions Analysis and Applications.**,
2, (2010), 155-166.

582. An improved convergence and
complexity for the interpolatory **Cubo Math. Journal**, 12, 1,
(2010), 151-161.

583. On the convergence of **PanAmerican
Math. J.**, 20, 1, (2010), 93-105.

584. On the feasibility of continuation
methods form solving equations, **ANVI**,
13, 1, (2010), 57-63.

585. Improved estimates on majorizing
sequences for the Newton-Kantorovich method, **J. Appl. Math. and Computing**, 32, (2010), 1-18.

586. On the semilocal convergence of a
Newton-type method of order three, **J.
Korea S. M. A. Ser. B.Pure and Appl. Math.**, 17, 1, (2010), 1-27.

587. A convergence analysis of Newton-like
method for singular equations using recurrent functions, **Numerical Functional Analysis and Optimization**, Issue31, 2, (2010),112-130.

588. Convergence conditions for the secant
method, **Cubo Math. Journal**, 12, 1,
(2010), 163-176.

589. A Kantorovich-type analysis of
Broyden’s method using recurrent functions, **J. Appl. Math. Computing**,32,2,(2010),353-

590. A generalized Kantorovich theorem for nonlinear equations
based on function splitting, **Rend. Circ.
Matem. Palerm**.2,58,3,(2009),441-451.

591. A new semilocal convergence Analysis
for a fast iterative method for nondifferentiable operators, **J. Appl. Math. and Computing.**,
DOI:10.1007/s12190-009-0303-0.

592. On **J.
Appl. Math. Comput.**, DOI:/j.amc.2009.07.005.

593. On a class of secant-like methods for
solving equations, **Numer. **,54,(2010),485-501.

594. On the Gauss-Newton method, J**. Appl. Math. Comput.**,35,1,(2011),537-.

595. On the convergence of **J. Complexity**,
DOI:10.1016/J.Co.2009.06.003.

596. A Kantorovich-type convergence analysis of The Newton-Josephy method for solving
variational inequalities ,**Numer.
Algorithms**, 55,(2010),447-466.

597. Tabatabaistic regression and its
applications to the space shuttle challenger O-ring data, **J. Appl. Math. and Computing**,33,(2010),513-523.

598. A Convergence analysis for directional two step Newton methods, **Numerical Algorithms**, 55,(2010),503-528.

599. Improved generalized
differentiability conditions for Newton-like methods, **J. Complexity,26,(2010),316-333.**

600. A Newton-like method for nonsmooth
variational inequalities, **Nonlinear
Analysis**: **T.M.A.**,
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601. Improved results on estimating and
extending the radius of the attraction ball, **Appl. Math. Letters**,23,(2010),404-408.

602. On **Aequationes Mathematicae**.,79,(2010),61-82.

603. On the solution of nonlinear equations
containing a nondifferentiable term, **East
Asian J. Math**., accepted.

604. Newton’s method and interior
point techniques, Pan Amer.Math.J.20,4,(2010),93-100.

605. An improved convergence analysis for
the Newton Kantorovich method under recurrence relations, **Intern J. Computer Math., **accepted.

606. Hummel-Seebeck method for generalized
equations under conditioned second Fréchet –derivative, **Nonlinear Functional Analysis and
Applications**, accepted.

607. Extending the application of the
shadowing lemma for operators with chaotic behavior,East Asian
Math.J.27,5,(2011),521-525.

608. On the convergence region of **Intern.
J. Computer Mathematics**, accepted.

609. Newton-like method for nonsmooth
subanalytic variational inequalities, **Mathematica**,52,75,1,(2010),5-13.

610. A semilocal convergence analysis for
directional **Mathematics of Computation**,
Amer. Math. Soc.,80,273,(2011),327-343.

611. Convergence conditions for
secant-type methods, **Chehoslovak J.Math**.,60,135,(2010),253-272.

612. On the convergence of Newton-type
methods using recurrent functions, **Intern
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613. On **Atti del Seminario Matematico e Fisico Dell”Universita
di Modena.,Regio Emilia,57,(2010),1-18.**

614.
On the semilocal convergence of
Newton-like methods using recurrent polynomials**, Revue D’Analyse Numérique et de la Théorie de l’Aprroximation**,
accepted.

615. On Newton’s method for solving
equations and function splitting, **Numerical
Mathematics: Theory methods and applications**,4,1,(2011),53-67.

616. On **J. Pure and Appl. Math.: Advances and
Applications**,3,1,(2010),1-16.

617. Secant-like method for solving
generalized equations, **Methods and
Applications of Analysis**,16,4,(2009),469-478.

__(J3) Submitted for Publication /Under
Preparation__

618. On the semilocal convergence of

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

620. On the monotone convergence of an iterative
method without derivatives.

621. On a unifying convergence analysis of
two-step two-point

622. On the solution of generalized
equations under Holder continuity conditions

623. A fast Dontchev-type iterative method
for solving generalized equations.

624. On the solution of nonsmooth
generalized equations.

625. On the convergence of

626. An improved convergence analysis of
one step intermediate Newton iterative scheme for nonlinear equationsJ.
Appl.Math.Computing,38,(2012),243-256.

627. A generalized Kantorovich theorem on
the solvability of nonlinear equation,Aequationes Mathematicae,77,1-2,(2009),99-105.

628. An intermediate

629. Newton-like methods with at least
quadratic order of convergence for the computation of fixed points,PUJM,43,(2011),8-18.

630. Majorizing functions and two point
Newton methods,J.Comput.Appl.Math.234,(2010),1473-1484.

631. Superquadratic method for generalized
equations under relaxed condition on the second Fréchet derivative.

632. Local convergence of Newton’s
method using Kantorovich majorants,Revue D’Analyse Numer.De
Th.Approx.2,(2010),97-106.

633. On the semilocal convergence of

634. An improved local convergence
analysis for secant –like method.

635. On the semilocal convergence of the
secant method with regularly continuous divided differences.

636. Newton’s method and regularly
smooth operator, Revue D’Analyse Numeriq.De Th.Approx.2,(2010)

637. On the semilocal convergence of
Newton-like methods using decreasing majorizing sequences.

638. On the semilocal convergence of

639. On the semilocal convergence of
Steffensen’s method using decreasing majorizing sequences.

640. On a theorem from interval analysis
for solving nonlinear equations,Australian J. Math. Anal.Applic..

641. On

642. On the Secant method for solving
equations containing nosmooth operators.

643.

644. On the conditioning of semidefinite
programs.

645.

646. Traub-Potra type method for
set-valued maps,Austral.J.Math.Anal.Applic.

647. On a generalization of Moret’s
theorem for inexact Newton-like methods,Pan Amer. Math. J.22,1,(2012),67-73.

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

649. On the Gausss-Newton method for
solving equation,Proyecciones J. Math.31,1,(2012),11-24.

650. Newton-Steffensen type method for
perturbed nonsmooth subanalytic variational inequalities.

651. Extending the Newton-Kantorovich
hypothesis for solving equations,J.Comput.Appl.math.234,10,(2010),2993-3006.

652. A Kantorovich-type analysis of
Broyden’s method using recurrent function,J.Appl.Math.Computing,32,2,(2010),353-.

653. On the semilocal convergence of
Werner’s method for solving
equations using recurrent function,PUJM,43,(2011),19-28.

654. On the convergence of Steffensen-type
method using recurrent functions,Revue D’Analyse Numerique et De
Th.Approx.38,2,(2009),130-143.

655. Inexact Newton-type
methods,J.Complexity(2010).

656. On the local convergence analysis of
inexact Gauss-Newton-like methods,Pan American J.Math.21,3,(2011),11-18.

657. On the convergence of Newton-like
methods for solving equations using slantly differentiable operators.

658. On the solution of generalized
equations and variational inequalities,Cubo,13,1,(2011),39-54.

659. On the midpoint method for solving
equations,Apl.Math.Comput.216,8,(2010),2321-2332.

660. On the semilocal convergence of the
Halley method using recurrent functions,J.Appl.Math.Computing,37,1,(2011),221-246.

661. On the semilocal convergence of
Newton’s method, when the
derivative is not continuously invertible,Cubo,13,1,(2011),39-54.

662. A note on the improvement of the
error bounds for a certain class of operators.

663. Locating roots for a certain class of
polynomial,East Asian math.J.26,1,(2010),351-363.

664. Weak sufficient convergence
conditions for some accelerated successive approximations.

665. Extending the applicability of a
Secant type method of order two using recurrent functions.

666. Local results for a continuous
analog of Newton’s method,East
Asian Math. J.3,26,(2010),365-370.

667. Improved results for continuous
modified Newton-type methods,Mathematica,53,76,1,(2011),1-14.

668. A derivative free quadratically
convergent iterative method for solving least squares problems,NUMA,58,(2011),555-571.

669. Kantorovich –type semilocal
convergence analysis for inexact Newton methods,J.Comput.Appl.math.235,11,(2011),2993-3005.

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

671. On an iterative method of Ulm-type
for solving equations.

672. On the convergence of inexact
Newton-type methods under weak conditions.

673. Directional secant type method for
solving equations.

674. A convergence analysis for
directional Newton-like methods,Communications on Applied Nonlinear Anal.18,4,(2011),24-38.

675. A comparison between two techniques
for directional cubically convergence Newton methods,NFAA.

676. Directional Chebyshev –type
methods for solving equations.

677. On the semilocal convergence of
efficient Chebyshev-secant-type methods,J.Comput.Appl.Math.235,10,(2011),3195-3206.

678. On the semilocal convergence of
Steffensen’s method<Mathematica 53,76,2,(2011),1-13.

679. A unified approach for the
convergence of a certain numerical algorithm using recurrent functions,Computing,90,3,(2010),131-164.

680. Semilocal convergence conditions for
the secant method using recurrent functions.

681. Newton-Steffensen methods for solving
generalized equations,Pan Amer.Math.J.21,2,(2011),45-57.

682. Convergence of directional Newton
methods undermild differentiability and applications,Applied Mathematics andComputation217,(2011),8731-8746.

683. Local convergence of a Secant
–type method for solving least square problems,Appl.Math.Comput.217,(2010),3816-3824.

684. Local convergence of a three point
method for solving least square problems,Numerical Functional Analysis and Applications,15,(2010),3816-3824.

685. On Newton’s method using
recurrent functions under hypotheses up to the second Frechet derivative,J.K.S.ME.

686. Convergence domains under
Zabrejko-Zincenko conditions for Newton-type methods using recurrent functions,Appl.Math.38,2,(2011),193-209.

687. On the solution of systems of
equations with constant rank derivatives,Numer. Algor.

688. Semilocal convergence of
Newton’s method for singular systems with constant rank derivatives,J.Korean
Soc.Math.Ed.Ser.B.Pure and Appl.Math.18,2,(2011),.

689. Newton-type methods,Advances in Nonlinear Variational Inequalities,14,2,(2011),65-79.

690. Newton Kantorovich approximations
under weak continuity condition,J.Appl.Math. Computing,37,1,(2011),361-375.

691. Newton-type method in K-normed spaces,Numer.
Funct.Anal. Applic.

692. On the semilocal convergence of the
Gauss-Newton method using recurrent functions,J.KSME,Ser.B.17,4,(2010),307-319.

693. A unifying theorem for Newton’s method on spaces with a
convergence structure,J.Complexity,(2010).

694. Convergence radius of the modified
Newton method for multiple zeros under Holder continuous derivative,Appl.Math.Comput.2,217,(2010),612-621.

695. Sixth order derivative free family of
iterative method,Appl.math.Comput..

696. A relationship between Lipschitz constants
appearing in Taylor’s formula,J.Korean math. Soc.math. Educ.Ser.B.Pure
and Applied math.18,4,(2011),345-351.

697. On the convergence of Newton’s
method under w^*-conditioned second derivative,Appl.Math.38,3,(2011),341-355.

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

699. Variational inequalities problems and
fixed point problems,computers and mathematics with applications
60,(2010),2292-2301.

700. On the quadratic convergence of
Newton’s method under center-Lipschitz but not necessarily Lipschitz
hypotheses.

701. On the convergence of Newton-like
methods using outer inverses but no Lipschitz condition,Nonlin.Funct.Anal.Applic.

702. A note on the iterative regularized
Gauss-Newton method under center-Lipschitz conditions,Commun.Appl.Non.Anal.18,4,(20011),89-96.

703. A note on a method for solving
inverse problems.

704. On the convergence of inexact
two-step Newton-type methods using
recurrent functions,East Asian J. math.27,3,(2011),319-338.

705. On the convergence of inexact two-step
Newton-like algorithms using recurrent functions,J.Appl.Math. Computing,38,1,(2012),,41-61.

706. A new convergence analysis for the
two step Newton method of order three.

707. A new convergence analysis for the
two step Newton method of order four.

708. Inexact Newton methods and recurrent
functions,Appl.Math.37,1,(2010),113-126.

709. A new semilocal convergence analysis
for the Jarratt method.

710. Extending the applicability of the
Gauss Newton method under average Lipschitz –type conditions,Numer. Algor.,DOI:10.1007/s11075-011-9466-9.

711. On the semilocal convergence of
Newton’s method using majorants and recurrent functions,Numer.Funct.Anal.Applic.

712. Chebyshev-Secant –type methods
for nondifferentiable operators

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

714. On the radius of convergence of some
Newton-type methods in Banach spaces,J.Korean Math. Soc.Ser. B.18,3,(2011),

715. On the semilocal convergence of an
inverse free Broyden’s method,PanAmer. Math.J.20,4,(2010),77-92.

716. Extended sufficient semilocal
convergence conditions for the secant method,Computers and Math.with Appl.
62,(2011),599-610.

717. On the convergence of Broyden’s
method in Hilbert space.

718. On the Halley method,Applic. Math.

719. Improved local analysis for a certain
class of iterative methods with cubic convergence,Numa.

720. Optimal Newton-type methods for
solving nonlinear equations,Advanc. Non.Variat. Ineq.14,1,(2011),47-59.

721. Ball convergence theorems for
Halley’s method in Banach spaces.J.Appl.math.Comput. 38,1,(2012),453-465.

722. Improved ball convergence of
Newton’s method under general conditions,Appl.Math.

723. On the semilocal convergence of
derivative free methods for solving equations.

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

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

726. Chebyshev-Kurchatov-type methods for
solving equations with non-diffeentiable operators.

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

728. Weak convergence conditions for Newton-like
methods

729. Weaker w-convergence conditions for
the Newton-Kantorovich method.

730. An intermediate Newton-Kantorovich
method for solving nonlinear equations

731. Unified majorizing sequences for
Traub-type multipoint iterative procedures.

732. New convergence conditions for the
secant method.

733. Majorizing sequences for iterative
methods.J.Comput.Appl.Math.(2011).

734. On the method of chord for solving
nonlinear equations.

735. Majorizing sequences of arbitrary
high convergence order for iterative procedures.

736. Improved local convergence of
Newton’s method under weak majorant condition,J.Comput. Appl.Math.
236,(2012),1892-1902.

737. Extending the applicability of the
mesh independence principle for solving nonlinear equations.

738. On the convergence of a Newton-like
method under weak conditions.Commun.Koren Math.Soc.26,4,(2011),575-584.

739. On the computation of fixed points for
random operator equations.

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

741. Extending the applicability of the
secant method and nondiscrete induction,Appl.math.Comput. 218,(2011),3238-3246.

742. Extending the applicability of
Newton’s method and nondiscrete induction,Applied Mathematics and
Computation,(2011)26-40.

743. Weaker conditions for the semilocal
convergence of Newton’s method,J.Complexity.

744. Extending the applicability of
Newton’s method under Holder differentiability conditions.

745. Secant-type methods and nondiscrete
induction.

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

747. How to develop fourth and seventh
order iterative methods.Novidad Sad J.
Math,40,2,(2010),61-67.

748. On the convergence of Broyden-like
methods using recurrent functions,Numer.Funct. Anal.Optimiz.32,1,(2011),26-40.

749. On the local convergence of inexact
Newton-like methods under residual control-type
conditions,J.Comput.Appl.math.235,(2010),218-228.

750. Weak convergence conditions for
inexact Newton-type methods,Applied Mathematics and computation,218,(2011),2800-2809.

751. Extending the applicability of
Newton’s method on Lie groups.

752. On the semilocal convergence of a
damped Newton’s method

753. On the convergence of Newton’s
method under uniformly continuity conditions

754. A unifying convergence analysis for
Newton’s method and twice Frechet differentiable operators.

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

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

757. Local convergence analysis of
proximal Newton-Gauss method

758. A finer discretization aand mesh
independence of Newton’s method for solving generalized equations.

759. New conditions for the convergence of
Newton-like methods and applications

760. Estimating upper bounds on the limit
points of majorizing sequences for Newton’s method

761. Weaker convergence conditions for the
secant method.

762. Weaker conditions for Newton’s
method under mild differentiability.

763. The majorant method in the theory of
Newton-Kantorovich approximations and generalized Lipschitz conditions

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

765. Majorizing sequences for
Newton’s method under centered conditions for the derivative.

766. Expanding the applicability of high
order-Traub-type procedures and their applications

767. Local convergence of efficient
secant-type methods for solving nonlinear equations,Applied Mathematics and
computation.

768. Efficient Steffensen-type algorithms
for solving nonlinear equations

769. An extension of Argyros’
Kantorovich-type solvability theorem for nonlinear equations,PAnAmer. Math.J.
22,1,(2012),57-66.

__(K) REPRINT(S) REQUESTS __

The following professors have requested papers:

1.
Etzio Venturino, University of

2. C.G. Lopez, Madeira, Portugal

3.
H. Jarchow, Institute fur Angewandte Mathematik der Universitat

4.
M.S. Khan,

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

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

7.
Josef Danes, Mathematical

8.
Goral Reddy, Dept. of Mathematics,

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

10.
Vlastimil Ptak,

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

12.
Dragan Jucic,

13.
Ahmad B. Casdam,

14.
Luis Saste Habana,

15.
S.N. Mishra,

16.
Josef Kral,

17.
Juan J. Nieto,

18.
S.D. Chatterji,

19.

20.
Ioan Muntean,

21.
S.L. Singh,

22.
P.D.N. Sriniras,

23.
S. Grzegorskii,

24.
Toma's Arechaga,

25.
J.D. Deader,

26.
P. Drouet,

27.
J. Weber, The

28.
David C. Kurtz,

29.
Jorge L. Quiroz, Colima,

30.
Ming-Po

31.
Mustafa Telci, Begtepe,

32.
Helmut Dietrich,

33.
Dong Chen,

34.

35.
M.S. Khan,

36.
Laszlo Mate,

37.
H.K. Pathak, Bhilai

38.
Osvaldo, Pino Garcia,

39.
B.K. Sharma,

40.
Aied Al-Knazi, King Abdul Aziz Univ.,

41.
Hassan-Qasin, King Abdul Aziz Univ.,

42.
Tadeusz Jankowski, University

43.
K. Kurzak,

44.
R. Gonzalez, 2000

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

46.
Prasad Balusu,

47.
Dieter Schott,

48.
J.M. Martinez,

49.

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

51.
W. Kliesch,

52.

53. Roman Brovsek, Ljubljana
Slovenia

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

55.
Donald Schaffner,

56.
David Ward, Barron Associates,

57.
Eugene Parker, Barron Associates,

58.
Miguel Gomez,

59.
L. Brueggemann,

60.
Fidel Delgado,

61.
B.C. Dhage,

62.
Leida Perea,

63.
David Ruch,

64.
Patrick J. Van Fleet,

65.
Tomas Arechaga, BS.

66.
M.A. Hernandez,

67.
J. Illuateau,

68.
Ioan A. Rus,

69.
V.K. Jain,

70.
Alan Lun,

71.
A.M. Saddeek,

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

73.
James L. Moseley,

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

75.
R.L.V. Gonzalez,

76.
Jose A. Ezquerro,

77.
N. Ramanujam,

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,

83.
Emil Catinas,

84.
Ion Pavaloiu,

85.
Th. Schauze,

86.
Ioan Lazar,

87.
Ch. Grossman,

88.
Livinus, Uko,

89.
Z. Athanassov, Bulgarian

90.
Zhenyu Huang,

91.

92.
L.J. Lardy,

93.
Kresimir Veselic, Lehrgebiet Mathematische Physik,

94.

95.
Vasudeva, Murthy,

96.
Adeyeye, S. Johnson C. Smith

97.Narasimham,Andhra,

98.Marius
Heljiu,Univ. Petrosani,

99.Nicolae
Todor,Oncology institute,

100.Pradid
Kumar Parida,

101.Nunchun,China.

102.Proinov,

103.Babajee Razin,Univ.
Mauritius,Mauritius.

104.Dr.
Athanasov,Bulgarian

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

__(L) ____Seminars__

At
the

__(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,

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.,

4.
Mathematical Association of

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,

7.
CAM 93,

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

10.
CAM 94,

11.
CAM 94,

12.
56th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical
Association of

13.
CAM 95,

14.
57th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical
Association of

15.
CAM 96,

16.
58th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association
of

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

18.
Regional #919 Meeting "Approximation in Mathematics" of the American
Mathematical Society in

19.
International Conference on Approximation and Optimization,

20.

21.
Research Day

22.
Oklahoma-Arkansas section of the

23.

24.
Regional Universities Research Day 2001. Poster Presentation, UCO,

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,

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,

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

30.
ANACM 2004,

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,

37.Research
Day 2006,UCO,December 1,2006,rescheduled for April 6,2007,Poster and abstract
presentation entitled:On an improved convergence analysis of

38.Participated
in the Supercomputing Conference :How to build the fastest super-computer in

October
3,2007,Norman OK,OU.

39.Oklahoma
Supercomputing Symposium, October 3,2007:Title:Fastest supercomputer twice in

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

41.
AMS Annual Meeting, January 6-9,2008,

and
Operations Applications Talk title: On the semilocal convergence of

42.
International Conference celebrating Popoviciu birthday.

points for

43.Paper
presentation Oklahoma Research day 2009,

Title:Enclosing roots of polynomials. A
talk was also given in the Torus conference ,

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,Oklahome Research Day 2011,CU,Lawton,Ok Novermber,2011.

__(N) ____Selected
Lectures Presented__

1. University of Georgia, 1982-1984

2. University of Iowa, 1984-1986

3.

4.
Northern

5. New Mexico State University, 1986-1990

6.

7.

8. University of New York, 1986-1988

9.

10.

11.

12.

13.

14.

__(O) ____Other
Meetings Attended__

1.
American Mathematical Society/Mathematical Association of

2.

3.
International Conference on Theory and Applications of Differential Equations,

4.
Annual Research Conferences of the Bureau of the Census,

__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,

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

(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

*(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

(3) I reviewed several Ph.D. theses of
students from the

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

(5) Included in the fourth and consequent
editions of "WHO'S WHO AMONG

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

(7) Nominated for the Faculty Hall of
Fame Award,

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

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

(10) Elected Member of the World
Coordinating Council of the Science and Academic Forum (SAF) (Nov. 2001) (11
members worldwide, 4 in

(11) Nominated for the "Hackler Award
for Teaching",

(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 :hiring,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.

5. Giving interviews to Lawton
Constitution,

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- Present.

__9. COMMUNITY SERVICE__

I
have been helping people from

__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

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

*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

__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

One
of the basic assumptions for the use of

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

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