Fixed Point Theory and Applications

✍ Scribed by Ravi P. Agarwal, Maria Meehan, Donal O’Regan

• Publisher: Cambridge University Press
• Year: 2001
• Tongue: English
• Leaves: 181
• Series: Cambridge Tracts in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Abstract......Page 2
Title page......Page 3
Copyright page......Page 4
Contents......Page 5
Preface......Page 8
1 Contractions......Page 12
2 Nonexpansive Maps......Page 23
3 Continuation Methods for Contractive and Nonexpansive Mappings......Page 30
4 The Theorems of Brouwer, Schauder and Monch......Page 39
5 Nonlinear Alternatives of Leray-Schauder Type......Page 59
6 Continuation Principles for Condensing Maps......Page 76
7 Fixed Point Theorems in Conical Shells......Page 89
8 Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces......Page 105
9 Contractive and Nonexpansive Multivalued Maps......Page 123
10 Multivalued Maps with Continuous Selections......Page 131
11 Multivalued Maps with Closed Graph......Page 141
12 Degree Theory......Page 153
Bibliography......Page 170
Index......Page 180