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基本説明
Offers the mathematical community an accessible, self-contained document that can be used as an introduction to the subject and its development. Contents - 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; and more.
Full Description
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.
Contents
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.
