Fixed Point Theory in Metric Spaces

1. Front Matter

   Pages i-xi

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2. Banach Contraction Principle and Applications

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 1-23

3. On Ran–Reurings Fixed Point Theorem

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 25-44

4. The Class of \((\alpha ,\psi )\)-Contractions and Related Fixed Point Theorems

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 45-66

5. Cyclic Contractions: An Improvement Result

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 67-78

6. The Class of JS-Contractions in Branciari Metric Spaces

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 79-87

7. Implicit Contractions on a Set Equipped with Two Metrics

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 89-100

8. On Fixed Points That Belong to the Zero Set of a Certain Function

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 101-122

9. A Coupled Fixed Point Problem Under a Finite Number of Equality Constraints

   • Praveen Agarwal, Mohamed Jleli, Bessem Samet

   Pages 123-138

10. JS-Metric Spaces and Fixed Point Results

    • Praveen Agarwal, Mohamed Jleli, Bessem Samet

    Pages 139-153

11. Iterated Bernstein Polynomial Approximations

    • Praveen Agarwal, Mohamed Jleli, Bessem Samet

    Pages 155-164

12. Back Matter

    Pages 165-166

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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.

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

“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)

• Department of Mathematics, Anand International College of Engineering, Jaipur, India

  Praveen Agarwal

• Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia

  Mohamed Jleli, Bessem Samet

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.

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