Multivalued Maps And Differential Inclusions Elements Of Theory And Applications

Author : Valeri Obukhovskii,Boris Gel'man
Publisher : World Scientific
Page : 221 pages
File Size : 46,7 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811220234

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Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications by Valeri Obukhovskii,Boris Gel'man Pdf

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.

Author : Valeri Obukhovskii,Boris Gel'man
Publisher : Unknown
Page : 208 pages
File Size : 45,8 Mb
Release : 2020
Category : Differential inclusions
ISBN : 9811220220

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Multivalued Maps And Differential Inclusions by Valeri Obukhovskii,Boris Gel'man Pdf

Author : Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca
Publisher : Walter de Gruyter
Page : 245 pages
File Size : 44,5 Mb
Release : 2011-07-20
Category : Mathematics
ISBN : 9783110870893

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Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces by Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca Pdf

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.

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 548 pages
File Size : 55,6 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9781402046667

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Topological Fixed Point Theory of Multivalued Mappings by Lech Górniewicz Pdf

This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.

Author : Aram V. Arutyunov,Valeri Obukhovskii
Publisher : Walter de Gruyter GmbH & Co KG
Page : 209 pages
File Size : 50,5 Mb
Release : 2016-12-05
Category : Mathematics
ISBN : 9783110460308

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Convex and Set-Valued Analysis by Aram V. Arutyunov,Valeri Obukhovskii Pdf

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 : J.-P. Aubin,A. Cellina
Publisher : Springer
Page : 342 pages
File Size : 53,6 Mb
Release : 2012-02-07
Category : Mathematics
ISBN : 3642695132

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Differential Inclusions by J.-P. Aubin,A. Cellina Pdf

Author : Dusan Repovs,P.V. Semenov
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 43,6 Mb
Release : 1998-09-30
Category : Mathematics
ISBN : 9780792352778

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Continuous Selections of Multivalued Mappings by Dusan Repovs,P.V. Semenov Pdf

Consists of three relatively independent parts--theory, results, and applications. The first part is directed toward advanced math students who wish to get familiar with the foundations of the theory. The second part surveys the existing results on continuous selections of multivalued mappings. It is intended for specialists in the area and for those who have mastered the first part. The third part collects examples of applications of continuous selections that have played a key role in the corresponding areas of mathematics. It is written for researchers in general and geometric topology, functional and convex analysis, approximation theory and fixed-point theory, differential inclusions, and mathematical economics. Annotation copyrighted by Book News, Inc., Portland, OR

Author : J. Andres,Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 771 pages
File Size : 41,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401704076

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Topological Fixed Point Principles for Boundary Value Problems by J. Andres,Lech Górniewicz Pdf

The book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topological fixed point theory in non-metric spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Therefore, three appendices concerning almost-periodic and derivo-periodic single-valued (multivalued) functions and (multivalued) fractals are supplied to the main three chapters.

Author : Constantin Corduneanu,Yizeng Li,Mehran Mahdavi
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 44,8 Mb
Release : 2016-03-25
Category : Mathematics
ISBN : 9781119189480

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Functional Differential Equations by Constantin Corduneanu,Yizeng Li,Mehran Mahdavi Pdf

Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

Author : Elimhan N Mahmudov
Publisher : Elsevier
Page : 396 pages
File Size : 55,5 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9780123884336

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Approximation and Optimization of Discrete and Differential Inclusions by Elimhan N Mahmudov Pdf

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Author : Donal O'Regan,Ravi P. Agarwal
Publisher : CRC Press
Page : 498 pages
File Size : 49,9 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 0203216490

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Set Valued Mappings with Applications in Nonlinear Analysis by Donal O'Regan,Ravi P. Agarwal Pdf

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 : Afif Ben Amar,Donal O'Regan
Publisher : Springer
Page : 194 pages
File Size : 50,8 Mb
Release : 2016-05-04
Category : Mathematics
ISBN : 9783319319483

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Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications by Afif Ben Amar,Donal O'Regan Pdf

This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of axiomatic measures of weak noncompactness. The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray–Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and both bounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games. Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors.

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 40,5 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Author : Xiao-qi Yang,Kok Lay Teo,Lou Caccetta
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475733334

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Optimization Methods and Applications by Xiao-qi Yang,Kok Lay Teo,Lou Caccetta Pdf

This edited book is dedicated to Professor N. U. Ahmed, a leading scholar and a renowned researcher in optimal control and optimization on the occasion of his retirement from the Department of Electrical Engineering at University of Ottawa in 1999. The contributions of this volume are in the areas of optimal control, non linear optimization and optimization applications. They are mainly the im proved and expanded versions of the papers selected from those presented in two special sessions of two international conferences. The first special session is Optimization Methods, which was organized by K. L. Teo and X. Q. Yang for the International Conference on Optimization and Variational Inequality, the City University of Hong Kong, Hong Kong, 1998. The other one is Optimal Control, which was organized byK. ~Teo and L. Caccetta for the Dynamic Control Congress, Ottawa, 1999. This volume is divided into three parts: Optimal Control; Optimization Methods; and Applications. The Optimal Control part is concerned with com putational methods, modeling and nonlinear systems. Three computational methods for solving optimal control problems are presented: (i) a regularization method for computing ill-conditioned optimal control problems, (ii) penalty function methods that appropriately handle final state equality constraints, and (iii) a multilevel optimization approach for the numerical solution of opti mal control problems. In the fourth paper, the worst-case optimal regulation involving linear time varying systems is formulated as a minimax optimal con trol problem.

Author : Jean Pierre Aubin,Arrigo Cellina
Publisher : Springer Verlag
Page : 342 pages
File Size : 48,5 Mb
Release : 1984
Category : Mathematics
ISBN : 0387131051

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Differential Inclusions by Jean Pierre Aubin,Arrigo Cellina Pdf