不動點理論導論（簡體書）

《不動點理論導論(英文版)》內容為：This book is intended as an introduction to fixed point theory and itsapplications. The topics treated range from fairly standard results （such asthe Principle of Contraction Mapping, Brouwers and Schauders fixedpoint theorems） to the frontier of what is known, but we have not tried toachieve maximal generality in all possible directions. We hope that thereferences quoted may be useful for this purpose.The point of view adopted in this book is that of functional analysis; forthe readers more interested in the algebraic topological point of view wehave added some references at the end of the book. A knowledge offunctional analysis is not a prerequisite, although a knowledge of anintroductory course in functional analysis would be profitable. However,the book contains two introductory chapters, one on general topology andanother on Banach and Hilbert spaces.本書是一部介紹不動點理論及其應用的入門教程。內容範圍廣闊，但並不是為增加書的篇幅而包括所有可能的結果，涉及從經典標準結果到最新前沿成果。本書採用了泛函分析的觀點，為了滿足更多讀者的要求，在書的末尾增加了代數拓撲一些資料。對泛函分析的瞭解不是學習本書的必需，但有一定的瞭解是很有益的。本書有介紹性的兩章，一章是關於基本拓撲，另一章是有關Banach和Hilbert空間。許多章節的末尾都增加了應用實例來加深對所學知識的理解。目次：拓撲空間和拓撲線性空間；Hilbert空間和Banach空間；壓縮原理；Brouwer不動點理論；Schauder不動點理論和一些概述；不放大映射不動點理論和有關映射類；映射序列和不動點；對偶映射和單調算子；映射族和不動點；不動點和集值映射；PM-空間中映射的不動點定理；拓撲度。
讀者對象：數學專業的高年級本科生和研究生以及相關專業的科研人員。

Editors Preface
Foreword
CHAPTER 1. Topological Spaces and Topological Linear Spaces
1.1. Metric Spaces
1.2. Compactness in Metric Spaces. Measures of Noncompactness
1.3. Baire Category Theorem
1.4. Topological Spaces
1.5. Linear Topological Spaces. Locally Convex Spaces
CHAPTER 2. Hilbert spaces and Banach spaces
2.1. Normed Spaces. Banach Spaces
2.2. Hilbert Spaces
2.3. Convergence in X, X* and L(X)
2.4. The Adjoint of an Operator
2.5. Classes of Banach Spaces
2.6. Measures of Noncompactness in Banach Spaces
2.7. Classes of Special Operators on Banach Spaces
CHAPTER 3. The Contraction Principle
3.0. Introduction
3.1. The Principle of Contraction Mapping in Complete Metric Spaces
3.2. Linear Operators and Contraction Mappings
3.3. Some Generalizations of the Contraction Mappings
3.4. Hilberts Projective Metric and Mappings of ContractiveType
3.5. Approximate Iteration
3.6, A Converse of the Contraction Principle
3.7. Some Applications of the Contraction Principle
CHAPTER 4. Brouwers Fixed Point Theorem
4.0. Introduction
4.1. The Fixed Point Property
4.2. Brouwers Fixed Point theorem. Equivalent Formulations
4.3. Robbins Complements of Brouwers Theorem
4.4. The Borsuk-Ulam Theorem
4.5. An Elementary Proof of Brouwers Theorem
4.6. Some Examples
4.7. Some Applications of Brouwers Fixed Point Theorem
4.8. The Computation of Fixed Points. Scarfs Theorem
CHAPTER 5. Schauders Fixed Point Theorem and Some Generalizations
5.0. Introduction
5.1. The Schauder Fixed Point Theorem
5.2. Darbos Generalization of Schauders Fixed Point Theorem
5.3. Krasnoselskiis, Rothes and Altmans Theorems
5.4. Browders and Fans Generalizations of Schauders and Tychonoffs Fixed Point Theorem
5.5. Some Applications
CHAPTER 6. Fixed Point Theorems for Nonexpansive Mappings and Related Classes of Mappings
6.0. Introduction
6.1. Nonexpansive Mappings
6.2. The Extension of Nonexpansive Mappings
6.3. Some General Properties of Nonexpansive Mappings
6.4. Nonexpansive Mappings on Some Classes of Banach Spaces
6.5. Convergence of Iterations of Nonexpansive Mappings
6.6. Classes of Mappings Related to Nonexpansive Mappings
6.7. Computation of Fixed Points for Classes of Nonexpansive Mappings
6.8. A Simple Example of a Nonexpansive Mapping on a Rotund Space Without Fixed Points
CHAPTER 7.Sequences of Mappings and Fixed Points
CHAPTER 8.Duality Masppings and Monotone Operators
CHAPTER 9.Families of Mappings and Fixed Points
CHAPTER 10.Fixed Points and Set-Valued Mappings
CHAPTER 11.Fixed Point Theorems for Mappings on PM-Spaces
CHAPTER 12.The Topological Degree
BIBLIOGRAHY
INDEX