Fixed point theory and applications

✍ Scribed by Agarwal R.P., Meehan M., O'Regan D.

• Publisher: CUP
• Year: 2001
• Tongue: English
• Leaves: 181
• Series: Cambridge Tracts in Mathematics
• 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
About......Page 2
Fixed Point Theory and Applications......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1 Contractions......Page 12
Exercises......Page 20
2 Nonexpansive Maps......Page 23
Exercises......Page 29
3 Continuation Methods for Contractive and Nonexpansive Mappings......Page 30
Exercises......Page 37
4 The Theorems of Brouwer, Schauder and Mönch......Page 39
Exercises......Page 56
5 Nonlinear Alternatives of Leray–Schauder Type......Page 59
Exercises......Page 74
6 Continuation Principles for Condensing Maps......Page 76
Exercises......Page 86
7 Fixed Point Theorems in Conical Shells......Page 89
Exercises......Page 103
8 Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces......Page 105
Exercises......Page 121
9 Contractive and Nonexpansive Multivalued Maps......Page 123
Exercises......Page 129
10 Multivalued Maps with Continuous Selections......Page 131
Exercises......Page 139
11 Multivalued Maps with Closed Graph......Page 141
Exercises......Page 150
12 Degree Theory......Page 153
Exercises......Page 168
Bibliography......Page 170
Index......Page 180