Download or read book The Computation of Fixed Points and Applications written by M. J. Todd and published by . This book was released on 2014-09-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Computation of Fixed Points and Applications written by Michael J. Todd and published by Springer. This book was released on 1976 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fixed Points written by Stepan Karamardian and published by Academic Press. This book was released on 2014-05-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Computation of Fixed Points and Applications written by M. J. Todd and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fixed Point Theory And Applications Proceedings Of The Second International Conference written by Kok Keong Tan and published by World Scientific. This book was released on 1992-08-08 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.
Download or read book Analysis and Computation of Fixed Points written by Stephen M. Robinson and published by Academic Press. This book was released on 2014-05-10 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
Download or read book Advances in Metric Fixed Point Theory and Applications written by Yeol Je Cho and published by Springer Nature. This book was released on 2021-06-05 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators. This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.
Download or read book Financial Cryptography and Data Security written by Radu Sion and published by Springer Science & Business Media. This book was released on 2010-07-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 14th International Conference on Financial Cryptography and Data Security, FC 2010, held in Tenerife, Canary Islands, Spain in January 2010. The 19 revised full papers and 15 revised short papers presented together with 1 panel report and 7 poster papers were carefully reviewed and selected from 130 submissions. The papers cover all aspects of securing transactions and systems and feature current research focusing on both fundamental and applied real-world deployments on all aspects surrounding commerce security.
Download or read book Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization written by D. Butnariu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive.
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 166 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.
Download or read book Fixed Points written by Stepan Karamardian and published by . This book was released on 1977 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing Equilibria and Fixed Points written by Zaifu Yang and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).
Download or read book Fixed Points written by I͡Uriĭ Alekseevich Shashkin and published by American Mathematical Soc.. This book was released on with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Functional Differential Equations and Approximation of Fixed Points written by H.-O. Peitgen and published by Springer. This book was released on 2006-11-15 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to Heinz Unger on occasion of his 65. birthday
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 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.
Download or read book Fixed Point Theory and Applications written by Kok-Keong Tan and published by World Scientific Publishing Company Incorporated. This book was released on 1992-01-01 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt:
