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Author: Donal O'Regan
Publisher: CRC Press
ISBN: 9780203216491
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Author: Donal O'Regan
Publisher: CRC Press
ISBN: 9780203216491
Category : Mathematics
Languages : en
Pages : 498
Get Book Here
Book Description
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Author: Donal O'Regan
Publisher: CRC Press
ISBN: 0203216490
Category : Mathematics
Languages : en
Pages : 480
Get Book Here
Book Description
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Author: Donal O'Regan
Publisher: CRC Press
ISBN: 9780415284240
Category : Mathematics
Languages : en
Pages : 480
Get Book Here
Book Description
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Author: Enayet Ullah Tarafdar
Publisher: World Scientific
ISBN: 9812704671
Category : Mathematics
Languages : en
Pages : 627
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Book Description
This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Author: Enayet U Tarafdar
Publisher: World Scientific
ISBN: 9814476218
Category : Mathematics
Languages : en
Pages : 627
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Book Description
This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Author: George Xian-Zhi Yuan
Publisher: CRC Press
ISBN: 9780824700317
Category : Mathematics
Languages : en
Pages : 648
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Book Description
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: Aram V. Arutyunov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110460300
Category : Mathematics
Languages : en
Pages : 209
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Book Description
This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents: Preface Part I: Convex analysis Convex sets and their properties The convex hull of a set. The interior of convex sets The affine hull of sets. The relative interior of convex sets Separation theorems for convex sets Convex functions Closedness, boundedness, continuity, and Lipschitz property of convex functions Conjugate functions Support functions Differentiability of convex functions and the subdifferential Convex cones A little more about convex cones in infinite-dimensional spaces A problem of linear programming More about convex sets and convex hulls Part II: Set-valued analysis Introduction to the theory of topological and metric spaces The Hausdorff metric and the distance between sets Some fine properties of the Hausdorff metric Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps A base of topology of the spaceHc(X) Measurable set-valued maps. Measurable selections and measurable choice theorems The superposition set-valued operator The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations Special selections of set-valued maps Differential inclusions Fixed points and coincidences of maps in metric spaces Stability of coincidence points and properties of covering maps Topological degree and fixed points of set-valued maps in Banach spaces Existence results for differential inclusions via the fixed point method Notation Bibliography Index
Author: Kung-Ching Chang
Publisher: Springer Science & Business Media
ISBN: 3540292322
Category : Mathematics
Languages : en
Pages : 448
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Book Description
This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.
Author: Singh
Publisher: CRC Press
ISBN: 9780824717902
Category : Mathematics
Languages : en
Pages : 498
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Book Description
In this innovative work, 43 distinguished contributors present the latest developments together with surveys of the field. Coverage encompasses several closely related disciplines and most of the results shown in this volume are unavailable in any other source. Among the important topics addressed are applications to the theory of ordinary differential equations of generalized order, degree theoretic methods in optimal control, numerical treatment of a nonlinear problem arising in heat transfer, and applications of fixed point theorems to problems in optimization and best approximation. Encouraging interdisciplinary research to stimulate further advances, Nonlinear Analysis and Applications serves as the vital reference for mathematicians, researchers, and graduate students engaged in applied mathematics, engineering, physics, industrial science, economics, optimization, probability, medicinal and operational research, and differential equations. Additionally, it is eminently suitable for use in professional seminars.
Author: W.A. Kirk
Publisher: Springer Science & Business Media
ISBN: 9401717486
Category : Mathematics
Languages : en
Pages : 702
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Book Description
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.
