Fixed Points
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Fixed Points
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Author : I͡Uriĭ Alekseevich Shashkin
language : en
Publisher: American Mathematical Soc.
Release Date :
Fixed Points written by I͡Uriĭ Alekseevich Shashkin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The theory of fixed points finds its roots in the work of Poincare, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory. This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts - such as continuity, compactness, degree of a map, and so on - are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic.
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.
Fixed Points
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Author : I︠U︡riĭ Alekseevich Shashkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Fixed Points written by I︠U︡riĭ Alekseevich Shashkin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Presents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.
Fixed Points
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Author : Stepan Karamardian
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Fixed Points written by Stepan Karamardian and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.
Fixed Points And Nonexpansive Mappings
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Author : Robert C. Sine
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Fixed Points And Nonexpansive Mappings written by Robert C. Sine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 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 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
The Computation Of Fixed Points And Applications
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Author : M. J. Todd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Computation Of Fixed Points And Applications written by M. J. Todd 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.
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixed-point algorithms to find many solutions to boundary-value problems.
Fixed Point Theory In Metric Spaces
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Author : Praveen Agarwal
language : en
Publisher: Springer
Release Date : 2018-10-13
Fixed Point Theory In Metric Spaces written by Praveen Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-13 with Mathematics categories.
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.
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.
Topics In Metric Fixed Point Theory
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Author : Kazimierz Goebel
language : en
Publisher: Cambridge University Press
Release Date : 1990
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 1990 with Mathematics categories.
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.