Topological Fixed Point Theory Of Multivalued Mappings

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 46,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401591959

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Topological Fixed Point Theory of Multivalued Mappings by Lech Górniewicz Pdf

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.

Author : Afif Ben Amar,Donal O'Regan
Publisher : Springer
Page : 194 pages
File Size : 51,6 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 : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 548 pages
File Size : 42,5 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 : J. Andres,Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 771 pages
File Size : 55,7 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 : Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 42,9 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9783319015866

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Topics in Fixed Point Theory by Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi Pdf

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 : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 54,8 Mb
Release : 2001-03-22
Category : Mathematics
ISBN : 9781139433792

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Fixed Point Theory and Applications by Ravi P. Agarwal,Maria Meehan,Donal O'Regan Pdf

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Author : Yeol Je Cho,Jong Kyu Kim
Publisher : Nova Publishers
Page : 222 pages
File Size : 47,6 Mb
Release : 2007
Category : Mathematics
ISBN : 1594548730

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Fixed Point Theory and Applications, Volume 6 by Yeol Je Cho,Jong Kyu Kim Pdf

Fixed Point Theory & Applications

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 43,7 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 1402032218

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Handbook of Topological Fixed Point Theory by Robert F. Brown Pdf

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.

Author : Robert F. Brown,Massimo Furi,L. Gorniewicz,Boju Jiang
Publisher : Springer Science & Business Media
Page : 966 pages
File Size : 44,9 Mb
Release : 2005-12-05
Category : Mathematics
ISBN : 9781402032226

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Handbook of Topological Fixed Point Theory by Robert F. Brown,Massimo Furi,L. Gorniewicz,Boju Jiang Pdf

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.

Author : Boju Jiang
Publisher : Springer
Page : 209 pages
File Size : 51,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468622

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Topological Fixed Point Theory and Applications by Boju Jiang Pdf

This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.

Author : Andrzej Fryszkowski
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 48,7 Mb
Release : 2006-02-21
Category : Mathematics
ISBN : 9781402024993

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Fixed Point Theory for Decomposable Sets by Andrzej Fryszkowski Pdf

Decomposable sets since T. R. Rockafellar in 1968 are one of basic notions in nonlinear analysis, especially in the theory of multifunctions. A subset K of measurable functions is called decomposable if (Q) for all and measurable A. This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property. Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.

Author : Afif Ben Amar,Donal O'Regan
Publisher : Springer Nature
Page : 258 pages
File Size : 49,7 Mb
Release : 2022-01-25
Category : Mathematics
ISBN : 9783030922047

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Topology and Approximate Fixed Points by Afif Ben Amar,Donal O'Regan Pdf

This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces—and fundamental properties of their topologies—are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.

Author : Jerzy Jezierski,Waclaw Marzantowicz
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 40,6 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9781402039317

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Homotopy Methods in Topological Fixed and Periodic Points Theory by Jerzy Jezierski,Waclaw Marzantowicz Pdf

The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.

Author : D. Repovs,P.V. Semenov
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 41,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401711623

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

This book is dedicated to the theory of continuous selections of multi valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as !'J-n area which has been intensively developing in recent decades and has found various applications in general topology, theory of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point theory, functional and convex analysis, game theory, mathematical economics, and other branches of modern mathematics. The fundamental results in this the ory were laid down in the mid 1950's by E. Michael. The book consists of (relatively independent) three parts - Part A: Theory, Part B: Results, and Part C: Applications. (We shall refer to these parts simply by their names). The target audience for the first part are students of mathematics (in their senior year or in their first year of graduate school) who wish to get familiar with the foundations of this theory. The goal of the second part is to give a comprehensive survey of the existing results on continuous selections of multivalued mappings. It is intended for specialists in this area as well as for those who have mastered the material of the first part of the book. In the third part we present important examples of applications of continuous selections. We have chosen examples which are sufficiently interesting and have played in some sense key role in the corresponding areas of mathematics.

Author : Dusan Repovs,P. V. Semenov
Publisher : Unknown
Page : 372 pages
File Size : 51,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401711631

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