Topics in Metric Fixed Point Theory

Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians.

Kazimierz Goebel (Author), W. A. Kirk (Author)

9780521382892, Cambridge University Press

Hardback, published 28 September 1990

256 pages
23.8 x 15.2 x 2.3 cm, 0.504 kg

"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

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.

Subject Areas: Calculus & mathematical analysis [PBK]