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Author : S. P. Singh,B. Watson,P Srivastava
Publisher : Unknown
Page : 236 pages
File Size : 48,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401588236
Author : S.P. Singh,B. Watson,P. Srivastava
Publisher : Springer
Page : 222 pages
File Size : 44,6 Mb
Release : 1997-09-30
Category : Mathematics
ISBN : 0792347587
The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.
Author : S.P. Singh,B. Watson,P. Srivastava
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 51,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401588225
The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.
Author : Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 52,6 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9783319015866
The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.
Author : W.A. Kirk,B. Sims
Publisher : Springer Science & Business Media
Page : 702 pages
File Size : 53,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401717489
Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers.
Author : Qamrul Hasan Ansari,Daya Ram Sahu
Publisher : Cambridge University Press
Page : 234 pages
File Size : 50,6 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781009351454
A book covering theory and examples for undergraduates, graduates, and researchers studying fixed point theory or nonlinear analysis.
Author : O. Hadzic,E. Pap
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 54,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401715607
Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
Author : S. A. Mohiuddine,M. Mursaleen,Dragan S. Djordjević
Publisher : CRC Press
Page : 222 pages
File Size : 41,5 Mb
Release : 2024-04-24
Category : Mathematics
ISBN : 9781040013366
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: • Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm • Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra • Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem • Discusses best proximity point results using measure of noncompactness and its applications • Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.
Author : George Xian-Zhi Yuan
Publisher : CRC Press
Page : 648 pages
File Size : 51,5 Mb
Release : 1999-02-09
Category : Mathematics
ISBN : 0824700317
This reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis.
Author : Ravi P. Agarwal,Donal O'Regan,D. R. Sahu
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 43,5 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9780387758183
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.
Author : K.P. Hart,Jun-iti Nagata,J.E. Vaughan
Publisher : Elsevier
Page : 537 pages
File Size : 55,7 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 9780080530864
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 216 pages
File Size : 40,9 Mb
Release : 2007-08
Category : Mathematics
ISBN : 1594548773
This volume deals with new topics in the areas of fixed point theory, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.
Author : Yu Qing Chen,Yeol Je Cho
Publisher : Nova Publishers
Page : 192 pages
File Size : 46,6 Mb
Release : 2004
Category : Mathematics
ISBN : 1594540675
This book primarily deals with non-linear operator theory in topological vector spaces and applications. Recently, non-linear functional analysis has become a main field of mathematics, which has played an important role in physics, mechanics and engineering, operations research and economics and many others for the past few decades. The book presents a survey of some main ideas, concepts, methods and applications in non-linear functional analysis.
Author : Qamrul Hasan Ansari
Publisher : Springer
Page : 362 pages
File Size : 45,7 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9788132218838
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Author : William Kirk,Naseer Shahzad
Publisher : Springer
Page : 173 pages
File Size : 54,8 Mb
Release : 2014-10-23
Category : Mathematics
ISBN : 9783319109275
This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.
