Fixed Point Theory in Metric Spaces
Recent Advances and Applications
Authors: Agarwal, Praveen, Jleli, Mohamed, Samet, Bessem
Free Preview Presents recent results on fixed point theory for cyclic mappings with applications to functional equations
 Discusses the RanReurings 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 KeliskyRivlin type result for qBernstein polynomials and modified qBernstein polynomials
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 About this book

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; RanReurings fixed point theorem with applications; the existence of fixed points for the class of αψ 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 wellknown fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for qBernstein polynomials and modified qBernstein polynomials.
The book is a valuable resource for a wide audience, including graduate students and researchers.  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 fixedpoint theory, partial differential equations, differential equations, fractional calculus, etc. He is the author/coauthor of more than 100 published papers in respected journals. He named as one of Thomson Reuters Highly Cited Researchers for 2015–2017.  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)
 Table of contents (10 chapters)


Banach Contraction Principle and Applications
Pages 123

On Ran–Reurings Fixed Point Theorem
Pages 2544

The Class of $$(\alpha ,\psi )$$Contractions and Related Fixed Point Theorems
Pages 4566

Cyclic Contractions: An Improvement Result
Pages 6778

The Class of JSContractions in Branciari Metric Spaces
Pages 7987

Table of contents (10 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Fixed Point Theory in Metric Spaces
 Book Subtitle
 Recent Advances and Applications
 Authors

 Praveen Agarwal
 Mohamed Jleli
 Bessem Samet
 Copyright
 2018
 Publisher
 Springer Singapore
 Copyright Holder
 Springer Nature Singapore Pte Ltd.
 eBook ISBN
 9789811329135
 DOI
 10.1007/9789811329135
 Hardcover ISBN
 9789811329128
 Softcover ISBN
 9789811348112
 Edition Number
 1
 Number of Pages
 XI, 166
 Number of Illustrations
 2 b/w illustrations
 Topics