Topological Fixed Point Theory And Applications

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Topological Fixed Point Theory of Multivalued Mappings

Lech Górniewicz
Topological Fixed Point Theory of Multivalued Mappings Book PDF

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 49,5 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.

Fixed Point Theory and Applications

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

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 47,9 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.

Fixed Point Theory and Applications, Volume 6

Yeol Je Cho,Jong Kyu Kim
Fixed Point Theory and Applications Volume 6 Book PDF

Author : Yeol Je Cho,Jong Kyu Kim
Publisher : Nova Publishers
Page : 222 pages
File Size : 42,6 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

Fixed Point Theory for Lipschitzian-type Mappings with Applications

Ravi P. Agarwal,Donal O'Regan,D. R. Sahu
Fixed Point Theory for Lipschitzian type Mappings with Applications Book PDF

Author : Ravi P. Agarwal,Donal O'Regan,D. R. Sahu
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 49,9 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9780387758183

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Fixed Point Theory for Lipschitzian-type Mappings with Applications by Ravi P. Agarwal,Donal O'Regan,D. R. Sahu Pdf

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.

Topological Fixed Point Theory and Applications

Boju Jiang
Topological Fixed Point Theory and Applications Book PDF

Author : Boju Jiang
Publisher : Springer
Page : 209 pages
File Size : 52,5 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.

Fixed Point Theory in Ordered Sets and Applications

Siegfried Carl,Seppo Heikkilä
Fixed Point Theory in Ordered Sets and Applications Book PDF

Author : Siegfried Carl,Seppo Heikkilä
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 45,9 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441975850

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Fixed Point Theory in Ordered Sets and Applications by Siegfried Carl,Seppo Heikkilä Pdf

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Fixed Point Theory and Applications

Yeol Je Cho
Fixed Point Theory and Applications Book PDF

Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 216 pages
File Size : 47,7 Mb
Release : 2007-08
Category : Mathematics
ISBN : 1594548773

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Fixed Point Theory and Applications by Yeol Je Cho Pdf

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.

Handbook of Topological Fixed Point Theory

Robert F. Brown
Handbook of Topological Fixed Point Theory Book PDF

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 45,9 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.

Topological Fixed Point Theory of Multivalued Mappings

Lech Górniewicz
Topological Fixed Point Theory of Multivalued Mappings Book PDF

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 548 pages
File Size : 48,9 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.

Fixed Point Theory and Its Applications

Robert F. Brown
Fixed Point Theory and Its Applications Book PDF

Author : Robert F. Brown
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 41,9 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850800

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Fixed Point Theory and Its Applications by Robert F. Brown Pdf

Fixed point theory touches on many areas of mathematics, such as general topology, algebraic topology, nonlinear functional analysis, and ordinary and partial differential equations and serves as a useful tool in applied mathematics. This book represents the proceedings of an informal three-day seminar held during the International Congress of Mathematicians in Berkeley in 1986. Bringing together topologists and analysts concerned with the study of fixed points of continuous functions, the seminar provided a forum for presentation of recent developments in several different areas. The topics covered include both topological fixed point theory from both the algebraic and geometric viewpoints, the fixed point theory of nonlinear operators on normed linear spaces and its applications, and the study of solutions of ordinary and partial differential equations by fixed point theory methods.Because the papers range from broad expositions to specialized research papers, the book provides readers with a good overview of the subject as well as a more detailed look at some specialized recent advances.

Fixed Point Theory

Andrzej Granas,James Dugundji
Fixed Point Theory Book PDF

Author : Andrzej Granas,James Dugundji
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 44,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387215938

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Fixed Point Theory by Andrzej Granas,James Dugundji Pdf

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS

Fixed Point Theory for Decomposable Sets

Andrzej Fryszkowski
Fixed Point Theory for Decomposable Sets Book PDF

Author : Andrzej Fryszkowski
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 53,6 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.

Topological Fixed Point Principles for Boundary Value Problems

J. Andres,Lech Górniewicz
Topological Fixed Point Principles for Boundary Value Problems Book PDF

Author : J. Andres,Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 771 pages
File Size : 40,6 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.

Fixed Point Theorems and Applications

Vittorino Pata
Fixed Point Theorems and Applications Book PDF

Author : Vittorino Pata
Publisher : Springer Nature
Page : 171 pages
File Size : 47,9 Mb
Release : 2019-09-22
Category : Mathematics
ISBN : 9783030196707

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Fixed Point Theorems and Applications by Vittorino Pata Pdf

This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.

Elementary Fixed Point Theorems

P.V. Subrahmanyam
Elementary Fixed Point Theorems Book PDF

Author : P.V. Subrahmanyam
Publisher : Springer
Page : 302 pages
File Size : 43,5 Mb
Release : 2019-01-10
Category : Mathematics
ISBN : 9789811331589

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Elementary Fixed Point Theorems by P.V. Subrahmanyam Pdf

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky’s theorem on periodic points, Thron’s results on the convergence of certain real iterates, Shield’s common fixed theorem for a commuting family of analytic functions and Bergweiler’s existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski’s theorem by Merrifield and Stein and Abian’s proof of the equivalence of Bourbaki–Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward’s theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka’s proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy–Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder–Gohde–Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.