Fixed Point Theory And Graph Theory
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Topological Fixed Point Theory Of Multivalued Mappings
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Author : Lech Górniewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Topological Fixed Point Theory Of Multivalued Mappings written by Lech Górniewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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.
Fixed Point Theory And Graph Theory
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Author : Monther Alfuraidan
language : en
Publisher: Academic Press
Release Date : 2016-06-20
Fixed Point Theory And Graph Theory written by Monther Alfuraidan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. - Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments - Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach - Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications
Fixed Point Theory
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Author : Vasile I. Istrățescu
language : en
Publisher: D Reidel Publishing Company
Release Date : 1981
Fixed Point Theory written by Vasile I. Istrățescu and has been published by D Reidel Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Fixed Point Theory
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Author : Andrzej Granas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fixed Point Theory written by Andrzej Granas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non linear functional analysis, emphasizing developments related to the Leray Schauder theory. Using for the most part geometric methods, our study cen ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-11
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with Mathematics categories.
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Fixed Point Theory And Applications
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Author : Ravi P. Agarwal
language : en
Publisher: Cambridge University Press
Release Date : 2001-03-22
Fixed Point Theory And Applications written by Ravi P. Agarwal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-22 with Mathematics categories.
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.
Elementary Fixed Point Theorems
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Author : P.V. Subrahmanyam
language : en
Publisher: Springer
Release Date : 2019-01-10
Elementary Fixed Point Theorems written by P.V. Subrahmanyam and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Mathematics categories.
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 viaa 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.
Fixed Point Theorems
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Author : D. R. Smart
language : en
Publisher: CUP Archive
Release Date : 1980-02-14
Fixed Point Theorems written by D. R. Smart and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-02-14 with Mathematics categories.
Topics In Metric Fixed Point Theory
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Author : Kazimierz Goebel
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-05
Topics In Metric Fixed Point Theory written by Kazimierz Goebel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-05 with Mathematics categories.
Metric fixed point theory has proved a flourishing area of research for the past twenty-five years. This book offers the mathematical community an accessible, self-contained document that can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including nonspecialists and provides a source for examples, references and new approaches for those currently working in the subject.
Fixed Point Theorems And Applications
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Author : Vittorino Pata
language : en
Publisher: Springer Nature
Release Date : 2019-09-22
Fixed Point Theorems And Applications written by Vittorino Pata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-22 with Mathematics categories.
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.