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Topological Fixed Point Theory And Applications
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Book Synopsis Topological Fixed Point Theory of Multivalued Mappings by : Lech Górniewicz
Download or read book Topological Fixed Point Theory of Multivalued Mappings written by Lech Górniewicz and published by Springer Science & Business Media. This book was released on 1999 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework.
Book Synopsis Fixed Point Theory for Lipschitzian-type Mappings with Applications by : Ravi P. Agarwal
Download or read book Fixed Point Theory for Lipschitzian-type Mappings with Applications written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory and Applications by : Ravi P. Agarwal
Download or read book Fixed Point Theory and Applications written by Ravi P. Agarwal and published by Cambridge University Press. This book was released on 2001-03-22 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory in Ordered Sets and Applications by : Siegfried Carl
Download or read book Fixed Point Theory in Ordered Sets and Applications written by Siegfried Carl and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theorems and Applications by : Vittorino Pata
Download or read book Fixed Point Theorems and Applications written by Vittorino Pata and published by Springer Nature. This book was released on 2019-09-22 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory and Applications by : Yeol Je Cho
Download or read book Fixed Point Theory and Applications written by Yeol Je Cho and published by Nova Publishers. This book was released on 2007-08 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Homotopy Methods in Topological Fixed and Periodic Points Theory by : Jerzy Jezierski
Download or read book Homotopy Methods in Topological Fixed and Periodic Points Theory written by Jerzy Jezierski and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory by : Andrzej Granas
Download or read book Fixed Point Theory written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Fixed Point Theory and Its Applications by : Robert F. Brown
Download or read book Fixed Point Theory and Its Applications written by Robert F. Brown and published by American Mathematical Soc.. This book was released on 1988 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Represents the proceedings of an informal three-day seminar held during the International Congress of Mathematicians in Berkeley in 1986. This work covers topics including topological fixed point theory from both the algebraic and geometric viewpoints, and the fixed point theory of nonlinear operators on normed linear spaces and its applications.
Book Synopsis Fixed Point Theory for Decomposable Sets by : Andrzej Fryszkowski
Download or read book Fixed Point Theory for Decomposable Sets written by Andrzej Fryszkowski and published by Springer Science & Business Media. This book was released on 2006-02-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Fixed Point Theory and Its Applications by :
Download or read book Topological Fixed Point Theory and Its Applications written by and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Fixed Point Theory and Applications by : Boju Jiang
Download or read book Topological Fixed Point Theory and Applications written by Boju Jiang and published by Springer. This book was released on 2006-11-14 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Fixed Point Theorems by : P.V. Subrahmanyam
Download or read book Elementary Fixed Point Theorems written by P.V. Subrahmanyam and published by Springer. This book was released on 2019-01-10 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advanced Fixed Point Theory for Economics by : Andrew McLennan
Download or read book Advanced Fixed Point Theory for Economics written by Andrew McLennan and published by Springer. This book was released on 2018-07-03 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.
Book Synopsis Topological Fixed Point Theory of Multivalued Mappings by : Lech Górniewicz
Download or read book Topological Fixed Point Theory of Multivalued Mappings written by Lech Górniewicz and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory in Probabilistic Metric Spaces by : O. Hadzic
Download or read book Fixed Point Theory in Probabilistic Metric Spaces written by O. Hadzic and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
Book Synopsis Fixed Point Theory in Metric Spaces by : Praveen Agarwal
Download or read book Fixed Point Theory in Metric Spaces written by Praveen Agarwal and published by Springer. This book was released on 2018-10-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials. The book is a valuable resource for a wide audience, including graduate students and researchers.
