Fixed Point Theory in Metric Spaces: Recent Advances and Applications by Praveen

Publisher Description

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.

Back Cover

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

Banach Contraction Principle and Applications.- On Ran-Reurings Fixed Point Theorem.- On a-y Contractive Mappings and Related Fixed Point Theorems.- Cyclic Contractions: An Improvement Result.- On JS-Contraction Mappings in Branciari Metric Spaces.- An Implicit Contraction on a Set Equipped with Two Metrics.- On Fixed Points that Belong to the Zero Set of a Certain Function.- A Coupled Fixed Point Problem Under a Finite Number of Equality Constraints.- The Study of Fixed Points in JS-Metric Spaces.- Iterated Bernstein Polynomial Approximations.

Review

"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." (Jarosaw Górnicki, zbMath 1416.54001, 2019)

Review Quote

"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." (Jaroslaw G

Feature

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

Details