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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Fixed Point Theory in Distance Spaces
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Fixed Point Theory in Distance Spaces
William Kirk, Naseer Shahzad (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
07.11.2014
Sprache
Englisch
EAN
9783319109268
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
William Kirk, Naseer Shahzad
Seitenanzahl
173
Einbandart
Gebundene Ausgabe
Autorenporträt
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
Schlagwörter
fixed point theory, metric spaces and geodesic shapes, metric spaces and geometric conditions, semimetric spaces, triangle inequalities
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBP - Topologie
PBWH - Mathematische Modellierung
TBJ - Mathematik für Ingenieure
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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