Fixed Point Theory for Lipschitzian-type Mappings with Applications

Ravi P. Agarwal

ISBN 10: 1441926062 / ISBN 13: 9781441926067

Edité par Springer New York, Springer US, 2010

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Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9781441926067

Détails bibliographiques

Titre : Fixed Point Theory for Lipschitzian-type ...

Éditeur : Springer New York, Springer US

Date d'édition : 2010

Reliure : Taschenbuch

Etat : Neu

A propos de ce titre

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.

Présentation de l'éditeur:

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.