Fixed Point Theory in Distance Spaces - Rilegato

Kirk, William; Shahzad, Naseer

Rilegato

ISBN 10: 331910926X ISBN 13: 9783319109268

Casa editrice: Springer Nature, 2014

Riassunto

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.

Su questo libro

Informazioni sull'autore

W. A. Kirk(1) Naseer Shahzad(2) (1) Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA E-mail address: william-kirk@uiowa.edu (2) Department of Mathematics, King Abdulaziz University, PO.Box 80203, Jeddah 21589, Saudi Arabia E-mail address: nshahzad@kau.edu.sa

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 331910926X
• ISBN 13: 9783319109268
• Rilegatura: Copertina rigida
• Numero di pagine: 188
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania