Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-07-21 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Metric Fixed Point Theory written by W.A. Kirk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide 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.
Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 966 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Analysis and Its Foundations written by Eric Schechter and published by Academic Press. This book was released on 1996-10-24 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
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.
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
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.
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.
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 2013-11-11 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Lefschetz Fixed Point Theorem written by Robert F. Brown and published by . This book was released on 1971 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Knot Theory written by William Menasco and published by Elsevier. This book was released on 2005-08-02 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics
Download or read book Topics in Metric Fixed Point Theory written by Kazimierz Goebel and published by Cambridge University Press. This book was released on 1990 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
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.
Download or read book Topological and Algebraic Structures in Fuzzy Sets written by S.E. Rodabaugh and published by Springer Science & Business Media. This book was released on 2003-09-30 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological and Algebraic Structures in Fuzzy Sets has these unique features: -strategically located at the juncture of fuzzy sets, topology, algebra, lattices, foundations of mathematics; -major studies in uniformities and convergence structures, fundamental examples in lattice-valued topology, modifications and extensions of sobriety, categorical aspects of lattice-valued subsets, logic and foundations of mathematics, t-norms and associated algebraic and ordered structures; -internationally recognized authorities clarify deep mathematical aspects of fuzzy sets, particularly those topological or algebraic in nature; -comprehensive bibliographies and tutorial nature of longer chapters take readers to the frontier of each topic; -extensively referenced introduction unifies volume and guides readers to chapters closest to their interests; -annotated open questions direct future research in the mathematics of fuzzy sets; -suitable as a text for advanced graduate students.
Download or read book Topological Methods in the Study of Boundary Value Problems written by Pablo Amster and published by Springer Science & Business Media. This book was released on 2013-10-23 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.
