Book contents
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Banach's Contraction Principle
- 3 Nonexpansive mappings: introduction
- 4 The basic fixed point theorems for nonexpansive mappings
- 5 Scaling the convexity of the unit ball
- 6 The modulus of convexity and normal structure
- 7 Normal structure and smoothness
- 8 Conditions involving compactness
- 9 Sequential approximation techniques for nonexpansive mappings
- 10 Weak sequential approximations
- 11 Properties of fixed point sets and minimal sets
- 12 Special properties of Hilbert space
- 13 Applications to accretivity
- 14 Ultrafilter methods
- 15 Set-valued mappings
- 16 Uniformly lipschitzian mappings
- 17 Rotative mappings
- 18 The theorems of Brouwer and Schauder
- 19 Lipschitzian mappings
- 20 Minimal displacement
- 21 The retraction problem
- Appendix: notes and comments
- References
- Index
2 - Banach's Contraction Principle
Published online by Cambridge University Press: 21 October 2009
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Banach's Contraction Principle
- 3 Nonexpansive mappings: introduction
- 4 The basic fixed point theorems for nonexpansive mappings
- 5 Scaling the convexity of the unit ball
- 6 The modulus of convexity and normal structure
- 7 Normal structure and smoothness
- 8 Conditions involving compactness
- 9 Sequential approximation techniques for nonexpansive mappings
- 10 Weak sequential approximations
- 11 Properties of fixed point sets and minimal sets
- 12 Special properties of Hilbert space
- 13 Applications to accretivity
- 14 Ultrafilter methods
- 15 Set-valued mappings
- 16 Uniformly lipschitzian mappings
- 17 Rotative mappings
- 18 The theorems of Brouwer and Schauder
- 19 Lipschitzian mappings
- 20 Minimal displacement
- 21 The retraction problem
- Appendix: notes and comments
- References
- Index
Summary
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- Chapter
- Information
- Topics in Metric Fixed Point Theory , pp. 7 - 26Publisher: Cambridge University PressPrint publication year: 1990