No Fixed Points
Author | : Nancy Reynolds |
Publisher | : |
Total Pages | : 928 |
Release | : 2021-02-09 |
Genre | : |
ISBN | : 9780300259322 |
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Author | : Nancy Reynolds |
Publisher | : |
Total Pages | : 928 |
Release | : 2021-02-09 |
Genre | : |
ISBN | : 9780300259322 |
Author | : I︠U︡riĭ Alekseevich Shashkin |
Publisher | : American Mathematical Soc. |
Total Pages | : 87 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 082189000X |
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.
Author | : Pierre E. Conner |
Publisher | : |
Total Pages | : 30 |
Release | : 1958 |
Genre | : Homeomorphisms |
ISBN | : |
Author | : Andrew McLennan |
Publisher | : Springer |
Total Pages | : 441 |
Release | : 2018-07-03 |
Genre | : Business & Economics |
ISBN | : 9811307105 |
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.
Author | : Kim C. Border |
Publisher | : Cambridge University Press |
Total Pages | : 144 |
Release | : 1985 |
Genre | : Business & Economics |
ISBN | : 9780521388085 |
This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.
Author | : Kazimierz Goebel |
Publisher | : Cambridge University Press |
Total Pages | : 258 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780521382892 |
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.
Author | : Andrzej Granas |
Publisher | : Springer Science & Business Media |
Total Pages | : 706 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 038721593X |
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
Author | : Ken Urai |
Publisher | : World Scientific |
Total Pages | : 311 |
Release | : 2010-05-13 |
Genre | : Mathematics |
ISBN | : 9814469181 |
This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.
Author | : M. J. Todd |
Publisher | : Springer Science & Business Media |
Total Pages | : 138 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3642503276 |
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.
Author | : Albrecht Dold |
Publisher | : Springer Science & Business Media |
Total Pages | : 398 |
Release | : 1995-02-15 |
Genre | : Mathematics |
ISBN | : 3540586601 |
Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.