不動點理論導論

《不動點理論導論》是2009年5月世界圖書出版公司出版的圖書，作者是伊斯特拉泰斯庫。本書主要介紹了不動點理論及其套用。

基本介紹

• 書名：不動點理論導論
• 出版社：世界圖書出版公司
• 出版時間：2009年5月1日
• 開本：24

圖書信息

外文書名: Fixed Point Theory: An Introduction

平裝: 446頁

正文語種: 英語

ISBN: 9787510004599, 7510004594

條形碼: 9787510004599

尺寸: 22 x 14.8 x 2.2 cm

重量: 567 g

作者簡介

作者：(美國)伊斯特拉泰斯庫

內容簡介

《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, Brouwer's and Schauder's 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.

目錄

Editor's 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. Hilbert's Projective Metric and Mappings of Contractive Type

3.5. Approximate Iteration

3.6. A Converse of the Contraction Principle

3.7. Some Applications of the Contraction Principle

CHAPTER 4. Brouwer's Fixed Point Theorem

4.0. Introduction

4.1. The Fixed Point Property

4.2. Brouwer's Fixed Point theorem. Equivalent Formulations

4.3. Robbins' Complements of Brouwer's Theorem

4.4. The Borsuk-Ulam Theorem

4.5. An Elementary Proof of Brouwer's Theorem

4.6. Some Examples

4.7. Some Applications of Brouwer's Fixed Point Theorem

4.8. The Computation of Fixed Points. Scarf's Theorem

CHAPTER 5. Schauder's Fixed Point Theorem and Some Generalizations

5.0. Introduction

5.1. The Schauder Fixed Point Theorem

5.2. Darbo's Generalization of Schauder's Fixed Point Theorem

5.3. Krasnoselskii's, Rothe's and Altman's Theorems

5.4. Browder's and Fan's Generalizations of Schauder's and Tychonoff's Fixed Point Theorem

5.5. Some Applications

CHAPTER 6. Fixed Point Theorems jbr 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

7.0. Introduction

7.1. Convergence of Fixed Points for Contractions or Related Mappings

7.2. Sequences of Mappings and Measures of Noncompactness

CHAPTER 8. Duality Mappings amt Monotome Operators

8.0. Introduction

8.1. Duality Mappings

8.2. Monotone Mappings and Classes of Nonexpansive Mappings

8.3. Some Surjectivity Theorems on Real Banach Spaces

8.4. Some Surjectivity Theorems in Complex Banach Spaces

8.5. Some Surjectivity Theorems in Locally Convex Spaces

8.6. Duality Mappings and Monotonicity for Set-Valued Mappings

8.7. Some Applications

CHAPTER 9. Families of Mappings and Fixed Points

9.0. Introduction

9.1. Markov's and Kakutani's Results

9.2. The RylI-Nardzewski Fixed Point Theorem

9.3. Fixed Points for Families of Nonexpansive Mappings

9.4. lnvariant Means on Semigroups and Fixed Point for Families of Mappings

CHAPTER 10. Fixed Points and Set-Valued Mappings

10.0 Introduction

10.1 The Pompeiu-Hausdorff Metric

10.2. Continuity for Set-Valued Mappings

10.3. Fixed Point Theorems for Some Classes of Set-valued Mappings

10.4. Set-Valued Contraction Mappings

10.5. Sequences of Set-Valued Mappings and Fixed Points

CHAPTER 11. Fixed Point Theorems for Mappings on PM-Spaces

11.0. Introduction

11.1. PM-Spaces

11.2. Contraction Mappings in PM-Spaces

11.3. Probabilistic Measures of Noncompactness

11.4. Sequences of Mappings and Fixed Points

CHAPTER 12. The Topological Degree

12.0.Introduction

12.1. The Topological Degree in Finite-Dimensional Spaces

12.2. The Leray-Schauder Topological Degree

12.3. Leray's Example

12.4. The Topological Degree for k-Set Contractions

12.5. The Uniqueness Problem for the Topological Degree

I2.6. The Computation of the Topological Degree

12.7. Some Applications of the Topological Degree

BIBLIOGRAPHY

INDEX