An Introduction To Metric Spaces And Fixed Point Theory

Author: Mohamed A. Khamsi
Editor: John Wiley & Sons
ISBN: 9780471418252
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Presents up-to-date Banach space results. * Features an extensive bibliography for outside reading. * Provides detailed exercises that elucidate more introductory material.

Fixed Point Theory In Distance Spaces

Author: William Kirk
Editor: Springer
ISBN: 3319109278
File Size: 36,78 MB
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This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.

Canadian Mathematical Bulletin

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File Size: 57,76 MB
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The Encyclopaedia Britannica

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File Size: 75,44 MB
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The Encyclop Dia Britannica

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File Size: 66,17 MB
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Mathematical Reviews

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Canadian Mathematical Bulletin

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Fixed Point Theory And Graph Theory

Author: Monther Alfuraidan
Editor: Academic Press
ISBN: 0128043652
File Size: 39,28 MB
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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

Canadian Mathematical Bulletin

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Proceedings Of The Symposium On Distribution Theory Held On 24 26 May 1991 At Kochi Kerala India

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The Encyclopaedia Britannica

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Scientiae Mathematicae Japonicae

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Seminar On Fixed Point Theory Cluj Napoca

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Nonstandard Methods In Fixed Point Theory

Author: Asuman G. Aksoy
Editor: Springer
ISBN: 9780387973647
File Size: 17,75 MB
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A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic results which follow. Set theoretic and Banach space ultraproducts constructions are studied in detail in the second part of the book, while the remainder of the book gives an introduction to the classical fixed point theory in addition to a discussion of normal structure. This is the first book which studies classical fixed point theory for non-expansive maps in the view of non-standard methods.

New Zealand Journal Of Mathematics

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The Theory Of Quantum Mechanics

Author: Edward Lee Hill
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File Size: 63,69 MB
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