Fixed Point Theory for Lipschitzian-Type Mappings with Applications

ISBN-13: 9781441926067 / Angielski / Miękka / 2010 / 368 str.

Springer

Opis

Over the past few decades, fixed point theory has become an important field of study in both pure and applied mathematics. This book presents the main techniques and results in the theory, from preliminary topics and basic results to applicable problems.

Recenzje

From the reviews: "The present book explains many of the basic techniques and ... the classical results of fixed point theory, and normal structure properties. ... Exercises are included in each chapter. As such, it is a self-contained book that can be used in a course for graduate students." (Srinivasa Swaminathan, Zentralblatt MATH, Vol. 1176, 2010) "This book provides a presentation of fixed point theory for Lipschitzian type mappings in metric and Banach spaces. ... An exercise section is included at the end of each chapter, containing interesting and well chosen material in order to cover topics complementing the main body of the text. ... It is worthwhile to point out that a beginner in this area is certainly well served with this text ... . A book including all ... topics together for sure should be welcomed for graduate students." (Enrique Llorens-Fuster, Mathematical Reviews, Issue 2010 e)

Spis treści

Fundamentals.- Convexity, Smoothness, and Duality Mappings.- Geometric Coefficients of Banach Spaces.- Existence Theorems in Metric Spaces.- Existence Theorems in Banach Spaces.- Approximation of Fixed Points.- Strong Convergence Theorems.- Applications of Fixed Point Theorems.

Blurb

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.