Fixed Points and Nonexpansive Mappings
Author: Robert C. Sine
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 264
ISBN-13: 0821850180
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Fixed Points and Nonexpansive Mappings
Fixed Point Theory for Lipschitzian-type Mappings with Applications
Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
Published: 2009-06-12
Total Pages: 373
ISBN-13: 0387758186
DOWNLOAD EBOOK →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.
Approximating Fixed Points and Fixed Point Sets of Nonexpansive Mappings in Banach Space
Topics in Metric Fixed Point Theory
Author: Kazimierz Goebel
Publisher: Cambridge University Press
Published: 1990
Total Pages: 258
ISBN-13: 9780521382892
DOWNLOAD EBOOK →Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.
Ergodic Theorems
Author: Ulrich Krengel
Publisher: Walter de Gruyter
Published: 2011-03-01
Total Pages: 369
ISBN-13: 3110844648
DOWNLOAD EBOOK →The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Fixed Points and Nonexpansive Mappings
Fixed Points for Nonexpansive Mappings with Orbital Conditions
Fixed Points of Nonlinear Operators
Author: Haiyun Zhou
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-06-08
Total Pages: 377
ISBN-13: 3110667096
DOWNLOAD EBOOK →Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.
Fixed Point Theory in Modular Function Spaces
Author: Mohamed A. Khamsi
Publisher: Birkhäuser
Published: 2015-03-24
Total Pages: 251
ISBN-13: 3319140515
DOWNLOAD EBOOK →This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.
