Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topological Fixed Point Theory and Its Applications, 6)

Agarwal, Ravi P.; O'Regan, Donal; Sahu, D. R.

ISBN 10: 0387758178 ISBN 13: 9780387758176

Published by Springer, 2009

Language: English

Condition: New Hardcover

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Bibliographic Details

Title

Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topological Fixed Point Theory and Its Applications, 6)

Publisher

Springer

Publication Date

2009

Language

English

ISBN 10

0387758178

ISBN 13

9780387758176

Binding

Hardcover

Condition

New

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Synopsis

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis.

This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields.

This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

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