Fixed Point Theory and Applications [Paperback]

This book provides a clear exposition of the flourishing field of fixed point theory.This book provides a clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, among others. Most of the main results and techniques are developed and applications in analysis are presented to illustrate the theory. Connections with topology are emphasised.Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject, with close to 100 exercises and a comprehensive bibliography.This book provides a clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, among others. Most of the main results and techniques are developed and applications in analysis are presented to illustrate the theory. Connections with topology are emphasised.Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject, with close to 100 exercises and a comprehensive bibliography.This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.Preface; 1. Contradictions; 2. Non-expansive maps; 3. Continuation methods for contractive and non-expansive mapping; 4. The theorems of Brouwer, Svhauder and Monch; 5. Non-linear alternatives of Leray-Schauder type; 6. Continuation principles for condensinlCÏ