Synopses & Reviews
Survey of fixed point theory for researchers and graduate students.
Synopsis
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.
Table of Contents
Preface; 1. Contractions; 2. Nonexpansive maps; 3. Continuation methods for contractive and nonexpansive maps; 4. The theorems of Brouwer, Schauder and Mönch; 5. Nonlinear alternatives of Leray-Schauder type; 6. Continuation principles for condensing maps; 7. Fixed point theorems in conical shells; 8. Fixed point theory in Hausdorff locally convex linear topological spaces; 9. Contractive and nonexpansive multivalued maps; 10. Multivalued maps with continuous selections; 11. Multivalued maps with closed graph; 12. Degree theory; Bibliography; Index.