Overview
- Presents many basic techniques and results in fixed point theory
- Self-contained presentation
- Good graduate text with exercises at the end of each chapter
Part of the book series: Topological Fixed Point Theory and Its Applications (TFPT, volume 6)
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About this book
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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Table of contents (8 chapters)
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Bibliographic Information
Book Title: Fixed Point Theory for Lipschitzian-type Mappings with Applications
Authors: D. R. Sahu, Donal O'Regan, Ravi P. Agarwal
Series Title: Topological Fixed Point Theory and Its Applications
DOI: https://doi.org/10.1007/978-0-387-75818-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Hardcover ISBN: 978-0-387-75817-6Published: 27 May 2009
Softcover ISBN: 978-1-4419-2606-7Published: 06 December 2010
eBook ISBN: 978-0-387-75818-3Published: 12 June 2009
Edition Number: 1
Number of Pages: X, 368
Topics: Analysis, Functional Analysis, Topology