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Author : Nancy Reynolds,Malcolm McCormick
Publisher : Unknown
Page : 907 pages
File Size : 48,5 Mb
Release : 2003
Category : Performing Arts
ISBN : 0300093667
Traces one hundred years of dance in Europe and North America, profiling dancer-choreographers, dance styles, and performance, before placing dance in a broader social and historical context.
Author : Nancy Reynolds,Malcolm McCormick
Publisher : Unknown
Page : 928 pages
File Size : 49,8 Mb
Release : 2021-02-09
Category : Electronic
ISBN : 0300259328
Author : I͡Uriĭ Alekseevich Shashkin
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 47,6 Mb
Release : 2024-05-03
Category : Mathematics
ISBN : 0821897284
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.
Author : Vasile Berinde
Publisher : Springer
Page : 326 pages
File Size : 50,6 Mb
Release : 2007-04-20
Category : Mathematics
ISBN : 9783540722342
This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.
Author : T. A. Burton
Publisher : Courier Corporation
Page : 366 pages
File Size : 42,8 Mb
Release : 2013-04-16
Category : Mathematics
ISBN : 9780486153322
The first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques, this text is suitable for advanced undergraduates and graduate students. 2006 edition.
Author : Andrzej Granas,James Dugundji
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387215938
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 : Pierre E. Conner,Edwin Earl Floyd
Publisher : Unknown
Page : 30 pages
File Size : 49,5 Mb
Release : 1958
Category : Homeomorphisms
ISBN : UOM:39015095249366
Author : Afif Ben Amar,Donal O'Regan
Publisher : Springer Nature
Page : 258 pages
File Size : 43,7 Mb
Release : 2022-01-25
Category : Mathematics
ISBN : 9783030922047
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces—and fundamental properties of their topologies—are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Author : Kazimierz Goebel,W. A. Kirk
Publisher : Cambridge University Press
Page : 258 pages
File Size : 48,5 Mb
Release : 1990
Category : Mathematics
ISBN : 0521382890
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 : Susin Nielsen
Publisher : Random House
Page : 261 pages
File Size : 53,6 Mb
Release : 2018-10-04
Category : Young Adult Fiction
ISBN : 9781787611481
Felix Knutsson is nearly thirteen, lives with his mother and pet gerbil Horatio, and is brilliant at memorising facts and trivia. So far, pretty normal. But Felix and his mom Astrid have a secret: they are living in a van. Astrid promises it’s only for a while until she finds a new job, and begs Felix not to breathe a word about it. So when Felix starts at a new school, he does his very best to hide the fact that most of his clothes are in storage, he only showers weekly at the community centre, and that he doesn’t have enough to eat. When his friends Dylan and Winnie ask to visit, Felix always has an excuse. But Felix has a plan to turn his and Astrid’s lives around: he’s going to go on his favourite game show Who, What, Where, When and win the cash prize. All he needs is a little luck and a lot of brain power . . . Susin Nielsen deftly combines humour, heartbreak, and hope in this moving story about people who slip through the cracks in society, and about the power of friendship and community to make all the difference.
Author : Zeraoulia Elhadj
Publisher : CRC Press
Page : 189 pages
File Size : 44,8 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9780429647420
Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Author : Robert F. Brown,Massimo Furi,L. Gorniewicz,Boju Jiang
Publisher : Springer Science & Business Media
Page : 972 pages
File Size : 55,7 Mb
Release : 2005-12-05
Category : Mathematics
ISBN : 9781402032226
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.
Author : Simeon Reich,David Shoiykhet
Publisher : Imperial College Press
Page : 374 pages
File Size : 48,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945755
Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.
Author : M. J. Todd
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783642503276
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 : Ken Urai
Publisher : World Scientific
Page : 311 pages
File Size : 45,5 Mb
Release : 2010
Category : Business & Economics
ISBN : 9789812837196
1. Introduction. 1.1. Mathematics is language. 1.2. Notes on some mathematical tools in this book. 1.3. Basic mathematical concepts and definitions -- 2. Fixed-point theorems. 2.1. Classical results and basic extensions. 2.2. Convexity and duality for general spaces. 2.3. Extension of classical results to general spaces -- 3. Nash equilibrium and abstract economy. 3.1. Multi-agent product settings for games. 3.2. Nash equilibrium. 3.3. Abstract economy -- 4. Gale-Nikaido-Debreu's theorem. 4.1. Gale-Nikaido-Debreu's theorem. 4.2. Market equilibria in general vector spaces. 4.3. Demand-supply coincidence in general spaces -- 5. General economic equilibrium. 5.1. General preferences and basic existence theorems. 5.2. Pareto optimal allocations. 5.3. Existence of general equilibrium -- 6. The C̮ech type homology theory and fixed points. 6.1. Basic concepts in algebraic topology. 6.2. Vietoris-Begle mapping and local connectedness. 6.3. Nikaido's analogue of Sperner's lemma. 6.4. Eilenberg-Montgomery's theorem -- 7. Convex structure and fixed-point index. 7.1. Lefschetz's fixed-point theorem and its extensions. 7.2. Cohomology theory for general spaces. 7.3. Dual-system structure and differentiability. 7.4. Linear Approximation for Isolated Fixed Points. 7.5. Indices for compact set of fixed points -- 8. Applications to related topics. 8.1. KKM, KKMS, and core existence. 8.2. Eaves' theorem. 8.3. Fan-Browder's coincidence theorem. 8.4. L-majorized mappings. 8.5. Variational inequality problem. 8.6. Equilibrium with cooperative concepts. 8.7. System of inequalities and affine transformations -- 9. Mathematics and social science. 9.1. Basic concepts in axiomatic set theory. 9.2. Individuals and rationality. 9.3. Society and values -- 10. Concluding discussions. 10.1. Fixed points and economic equilibria. 10.2. Rationality and fixed-point views of the world