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Fixed Point Theory in Metric Spaces

Recent Advances and Applications

  • Praveen Agarwal
  • Mohamed Jleli
  • Bessem Samet

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

  • Praveen Agarwal
    • 1
  • Mohamed Jleli
    • 2
  • Bessem Samet
    • 3
  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

Bibliographic information