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Fixed Point Theory in Metric Spaces

✍ Scribed by Praveen Agarwal, Mohamed Jleli, Bessem Samet

Publisher
Springer
Year
2018
Tongue
English
Leaves
173
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xi
Banach Contraction Principle and Applications (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 1-23
On Ran–Reurings Fixed Point Theorem (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 25-44
The Class of ((\alpha ,\psi ))-Contractions and Related Fixed Point Theorems (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 45-66
Cyclic Contractions: An Improvement Result (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 67-78
The Class of JS-Contractions in Branciari Metric Spaces (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 79-87
Implicit Contractions on a Set Equipped with Two Metrics (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 89-100
On Fixed Points That Belong to the Zero Set of a Certain Function (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 101-122
A Coupled Fixed Point Problem Under a Finite Number of Equality Constraints (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 123-138
JS-Metric Spaces and Fixed Point Results (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 139-153
Iterated Bernstein Polynomial Approximations (Praveen Agarwal, Mohamed Jleli, Bessem Samet)....Pages 155-164
Back Matter ....Pages 165-166

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