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© 2018

Fixed Point Theory in Metric Spaces

Recent Advances and Applications

Benefits

  • Presents recent results on fixed point theory for cyclic mappings with applications to functional equations

  • Discusses the Ran-Reurings fixed point theorem and its applications

  • Analyzes the recent generalization of Banach fixed point theorem on Branciari metric spaces

  • Addresses the solvability of a coupled fixed point problem under a finite number of equality constraints

  • Establishes a new fixed point theorem, which helps establish a Kelisky-Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials

Book

Table of contents

  1. Front Matter
    Pages i-xi
  2. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 1-23
  3. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 25-44
  4. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 45-66
  5. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 67-78
  6. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 79-87
  7. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 89-100
  8. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 101-122
  9. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 123-138
  10. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 139-153
  11. Praveen Agarwal, Mohamed Jleli, Bessem Samet
    Pages 155-164
  12. Back Matter
    Pages 165-166

About this book

Introduction

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials.

The book is a valuable resource for a wide audience, including graduate students and researchers.

Keywords

Banach Contraction Principle Ran-Reurings Fixed Point Theorem Contractive Mappings Cyclic Contractions Branciari Metric Spaces Implicit Contraction JS-Metric Spaces Bernstein Polynomial

Authors and affiliations

  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

About the authors

PRAVEEN AGARWAL is Professor at the Department of Mathematics, Anand International College of Engineering, Jaipur, India. He has published over 200 articles related to special functions, fractional calculus and mathematical physics in several leading mathematics journals. His latest research has focused on partial differential equations, fixed point theory and fractional differential equations. He has been on the editorial boards of several journals, including the SCI, SCIE and SCOPUS, and he has been involved in a number of conferences. Recently, he received the Most Outstanding Researcher 2018 award for his contribution to mathematics by the Union Minister of Human Resource Development of India, Prakash Javadekar. He has received numerous international research grants.

MOHAMED JLELI is Full Professor of Mathematics at King Saud University, Saudi Arabia. He obtained his PhD degree in Pure Mathematics entitled “Constant mean curvature hypersurfaces” from the Faculty of Sciences of Paris 12, France, in 2004. He has written several papers on differential geometry, partial differential equations, evolution equations, fractional differential equations and fixed point theory. He is on the editorial board of several international journals and acts as a referee for a number of international journals in mathematics.

BESSEM SAMET is Full Professor of Applied Mathematics at King Saud University, Saudi Arabia. He obtained his PhD degree in Applied Mathematics entitled “Topological derivative method for Maxwell equations and its applications” from Paul Sabatier University, France, in 2004. His research interests include various branches of nonlinear analysis, such as fixed-point theory, partial differential equations, differential equations, fractional calculus, etc. He is the author/co-author of more than 100 published papers in respected journals. He named as one of Thomson Reuters Highly Cited Researchers for 2015–2017.

Bibliographic information

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Reviews

“The book can be helpful for students and researchers interested in metric fixed point theory, with particular emphasis on the various extensions of the Banach contraction principle.” (Jarosław Górnicki, zbMath 1416.54001, 2019)