Fixed Point Theory and Applications

by Ravi P. Agarwal , Maria Meehan , Donal O'Regan

• ISBN13: 9780521802505
• ISBN10: 0521802504
• Format: Hardcover
• Copyright: 2001-04-09
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	vii
Contractions	1	(11)
Nonexpansive Maps	12	(7)
Continuation Methods for Contractive and Nonexpansive Mappings	19	(9)
The Theorems of Brouwer, Schauder and Monch	28	(20)
Nonlinear Alternatives of Leray-Schauder Type	48	(17)
Continuation Principles for Condensing Maps	65	(13)
Fixed Point Theorems in Conical Shells	78	(16)
Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces	94	(18)
Contractive and Nonexpansive Multivalued Maps	112	(8)
Multivalued Maps with Continuous Selections	120	(10)
Multivalued Maps with Closed Graph	130	(12)
Degree Theory	142	(17)
Bibliography	159	(10)
Index	169