Topics in Metric Fixed Point Theory: 28 (Cambridge Studies in Advanced Mathematics, Series Number 28)
Cambridge University Press, 10/4/1990
EAN 9780521382892, ISBN10: 0521382890
Hardcover, 256 pages, 23.9 x 15.2 x 2.3 cm
Language: English
Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.
Introduction
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
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
References.