handbook of metric fixed point theory

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Handbook Of Metric Fixed Point Theory

Author : William Kirk
ISBN : 9789401717489
Genre : Mathematics
File Size : 83. 12 MB
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Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers.

Handbook Of Topological Fixed Point Theory

Author : Robert F. Brown
ISBN : 1402032218
Genre : Mathematics
File Size : 87. 83 MB
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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.

Fixed Point Theory In Distance Spaces

Author : William Kirk
ISBN : 9783319109275
Genre : Mathematics
File Size : 41. 32 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.

Topological Fixed Point Theory Of Multivalued Mappings

Author : Lech Górniewicz
ISBN : 9781402046667
Genre : Mathematics
File Size : 67. 32 MB
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This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.

Fixed Point Theory For Weakly Contractive Maps Defined Implicitly Using Multiplicative C Class Functions

Author : Clement Ampadu
ISBN : 9781365924439
Genre :
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Handbook Of Applied Analysis

Author : Nikolaos S. Papageorgiou
ISBN : 9780387789071
Genre : Mathematics
File Size : 86. 68 MB
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This handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. It details many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features make the volume a valuable tool for every researcher working on nonlinear analysis.

Seminar Of Mathematical Analysis

Author : Daniel Girela Álvarez
ISBN : 8447208575
Genre : Mathematics
File Size : 70. 32 MB
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This volume consists of the lecture notes of the Seminar on Mathematical Analysis which was held at the Universities of Malaga and Seville, Septembre 2002-February 2003.

Mathematik Im Mittelalterlichen Islam

Author : J. L. Berggren
ISBN : 354076688X
Genre : Mathematics
File Size : 61. 87 MB
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Die Mathematik im mittelalterlichen Islam hatte großen Einfluss auf die allgemeine Entwicklung des Faches. Der Autor beschreibt diese Periode der Geschichte der Mathematik und bezieht sich dabei auf die arabischsprachigen Quellen. Zu den behandelten Themen gehören Dezimalrechnen, Geometrie, ebene und sphärische Trigonometrie, Algebra sowie die Approximation von Wurzeln von Gleichungen. Das Buch wendet sich an Mathematikhistoriker und -studenten, aber auch an alle Interessierten mit Mathematikkenntnissen der weiterführenden Schule.

Gazette Australian Mathematical Society

Author : Australian Mathematical Society
ISBN : UOM:39015056636957
Genre : Mathematics
File Size : 31. 96 MB
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Iterative Approximation Of Fixed Points

Author : Vasile Berinde
ISBN : 3540722335
Genre : Mathematics
File Size : 20. 95 MB
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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.

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