Topological And Approximation Methods Of Degree Theory Of Set Valued Maps
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Topological And Approximation Methods Of Degree Theory Of Set Valued Maps
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Author : Wojciech Kryszewski
language : en
Publisher:
Release Date : 1994
Topological And Approximation Methods Of Degree Theory Of Set Valued Maps written by Wojciech Kryszewski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Approximation theory categories.
Topological Fixed Point Theory Of Multivalued Mappings
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Author : Lech Górniewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Topological Fixed Point Theory Of Multivalued Mappings written by Lech Górniewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This book is an attempt to give a systematic presentation of results and meth ods which concern the fixed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to study ing topological methods in the fixed point theory of multivalued mappings and applications, mainly to differential inclusions. Thus in Chapter III the approximation (on the graph) method in fixed point theory of multi valued mappings is presented. Chapter IV is devoted to the homo logical methods and contains more general results, e. g. , the Lefschetz Fixed Point Theorem, the fixed point index and the topological degree theory. In Chapter V applications to some special problems in fixed point theory are formulated. Then in the last chapter a direct application's to differential inclusions are presented. Note that Chapter I and Chapter II have an auxiliary character, and only results con nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the fixed point theory. In the last section of our book (see Section 75) we give a bibliographical guide and also signal some further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and com mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. Gorka, M. Gorniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
Condensing Multivalued Maps And Semilinear Differential Inclusions In Banach Spaces
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Author : Mikhail I. Kamenskii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-20
Condensing Multivalued Maps And Semilinear Differential Inclusions In Banach Spaces written by Mikhail I. Kamenskii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.
The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.
Topological Methods For Set Valued Nonlinear Analysis
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Author : Enayet Ullah Tarafdar
language : en
Publisher: World Scientific
Release Date : 2008
Topological Methods For Set Valued Nonlinear Analysis written by Enayet Ullah Tarafdar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Multivalued Maps And Differential Inclusions Elements Of Theory And Applications
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Author : Valeri Obukhovskii
language : en
Publisher: World Scientific
Release Date : 2020-04-04
Multivalued Maps And Differential Inclusions Elements Of Theory And Applications written by Valeri Obukhovskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-04 with Mathematics categories.
The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields.This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics.The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies.
Handbook Of Topological Fixed Point Theory
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Author : Robert F. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Handbook Of Topological Fixed Point Theory written by Robert F. Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Mathematics categories.
This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
Juliusz Schauder Center Winter School On Methods In Multivalued Analysis
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Author : Lech Górniewicz
language : en
Publisher:
Release Date : 2006
Juliusz Schauder Center Winter School On Methods In Multivalued Analysis written by Lech Górniewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematical analysis categories.
Functional Analysis With Current Applications In Science Technology And Industry
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Author : Martin Brokate
language : en
Publisher: CRC Press
Release Date : 2021-02-28
Functional Analysis With Current Applications In Science Technology And Industry written by Martin Brokate and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-28 with Mathematics categories.
This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996. Topics include topological vector spaces, Banach algebras, meromorphic functions, partial differential equations, variational equations and inequalities, optimization, wavelets, elastroplasticity, numerical integration, fractal image compression, reservoir simulation, forest management, and industrial maths.
Topological Analysis
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Author : Martin Väth
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-29
Topological Analysis written by Martin Väth and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-29 with Mathematics categories.
This monograph aims to give a self-contained introduction into the whole field of topological analysis: Requiring essentially only basic knowledge of elementary calculus and linear algebra, it provides all required background from topology, analysis, linear and nonlinear functional analysis, and multivalued maps, containing even basic topics like separation axioms, inverse and implicit function theorems, the Hahn-Banach theorem, Banach manifolds, or the most important concepts of continuity of multivalued maps. Thus, it can be used as additional material in basic courses on such topics. The main intention, however, is to provide also additional information on some fine points which are usually not discussed in such introductory courses. The selection of the topics is mainly motivated by the requirements for degree theory which is presented in various variants, starting from the elementary Brouwer degree (in Euclidean spaces and on manifolds) with several of its famous classical consequences, up to a general degree theory for function triples which applies for a large class of problems in a natural manner. Although it has been known to specialists that, in principle, such a general degree theory must exist, this is the first monograph in which the corresponding theory is developed in detail.
Solution Sets For Differential Equations And Inclusions
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Author : Smaïl Djebali
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06
Solution Sets For Differential Equations And Inclusions written by Smaïl Djebali and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.