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Topics in Metric Fixed Point Theory

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Topics in Metric Fixed Point Theory

Topics in Metric Fixed Point Theory

Kazimierz Goebel
W. A. Kirk, University of Iowa
June 2008
Paperback
9780521064064
    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.

    Reviews & endorsements

    "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

    See more reviews

    Product details

    June 2008
    Paperback
    9780521064064
    256 pages
    229 × 150 × 15 mm
    0.378kg
    Available

    Often bought together

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    Fixed Point Theory and Applications

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    Metric Spaces

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    This title is available for institutional purchase via Cambridge Core

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    Contents

    Table of 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.
      • Show more

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