Fixed point theory for Lipschitzian-type mappings with applications

D. R. Sahu, Donal O’Regan, Ravi P. Agarwal (auth.)0387758178, 9780387758176

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.

Table of contents :
Front Matter….Pages 1-9
Fundamentals….Pages 1-47
Convexity, Smoothness, and Duality Mappings….Pages 49-125
Geometric Coefficients of Banach Spaces….Pages 127-174
Existence Theorems in Metric Spaces….Pages 175-209
Existence Theorems in Banach Spaces….Pages 211-278
Approximation of Fixed Points….Pages 279-313
Strong Convergence Theorems….Pages 315-331
Applications of Fixed Point Theorems….Pages 333-348
Back Matter….Pages 1-20