Fixed Point Theory and Applications

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Cambridge University Press, Mar 22, 2001 - Mathematics - 170 pages
This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. 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.
 

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Contents

2 Nonexpansive Maps
12
3 Continuation Methods for Contractive and Nonexpansive Mappings
19
4 The Theorems of Brouwe Schauder and Mönch
28
5 Nonlinear Alternatives of LeraySchauder Type
48
6 Continuation Principles for Condensing Maps
65
7 Fixed Point Theorems in Conical Shells
78
8 Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces
94
9 Contractive and Nonexpansive Multivalued Maps
112
10 Multivalued Maps with Continuous Selections
120
11 Multivalued Maps with Closed Graph
130
12 Degree Theory
142
Bibliography
159
Index
169
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