Measures of Noncompactness in Metric Fixed Point Theory

Overview

This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations. This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area. Most of the results presented here were obtained by...
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Overview

This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations. This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area. Most of the results presented here were obtained by the authors over the last ten years and have not previously appeared in any other textbook.
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Product Details

Table of Contents

Preface
Introduction 1
I The fixed point theorems of Brouwer and Schauder 5
II Measures of noncompactness 17
III Minimal sets for a measure of noncompactness 45
IV Convexity and smoothness 57
V Nearly uniform convexity and nearly uniform smoothness 85
VI Fixed points for nonexpansive mappings and normal structure 109
VII Fixed point theorems in the absence of normal structure 131
VIII Uniformly Lipschitzian mappings 141
IX Asymptotically regular mappings 153
X Packing rates and [phi]-contractiveness constants 167
References 197
Subject Index 205
List of Symbols and Notations 209
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