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Metric fixed point theory has proved a flourishing area of research for the past twenty-five years. This book offers the mathematical community an accessible, self-contained document that can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including nonspecialists and provides a source for examples, references and new approaches for those currently working in the subject.
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"In short, everything anyone wants to know about metric fixed point theory is discussed somewhere, clearly and with recent proofs where there are any." M. M. Day, Mathematical Reviews
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- Date Published: June 2008
- format: Paperback
- isbn: 9780521064064
- length: 256 pages
- dimensions: 229 x 150 x 15 mm
- weight: 0.378kg
- availability: Available
Table of Contents
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
10. Weak sequential approximations
11. Properties of fixed point sets and minimal sets
12. Special properties of Hilbert space
13. Applications to accretivity
14. Nonstandard 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
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