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The Resource Fixed point theory in distance spaces, William Kirk, Naseer Shahzad

Fixed point theory in distance spaces, William Kirk, Naseer Shahzad

Label
Fixed point theory in distance spaces
Title
Fixed point theory in distance spaces
Statement of responsibility
William Kirk, Naseer Shahzad
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Cataloging source
BTCTA
http://library.link/vocab/creatorName
Kirk, W. A
Index
index present
LC call number
QA329.9
LC item number
.K57 2014
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Shahzad, Naseer
http://library.link/vocab/subjectName
  • Fixed point theory
  • Topology
  • Fixed point theory
  • Topology
Label
Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 159-171) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- Part 1. Metric Spaces -- Introduction -- Caristi's Theorem and Extensions -- Nonexpansive Mappings and Zermelo's Theorem -- Hyperconvex metric spaces -- Ultrametric spaces -- Part 2. Length Spaces and Geodesic Spaces -- Busemann spaces and hyperbolic spaces -- Length spaces and local contractions -- The G-spaces of Busemann -- CAT(0) Spaces -- Ptolemaic Spaces -- R-Trees (metric trees) -- Part 3. Beyond Metric Spaces -- b-Metric Spaces -- Generalized Metric Spaces -- Partial Metric Spaces -- Diversities -- Bibliography -- Index
Control code
903490019
Dimensions
24 cm
Extent
xi, 173 pages
Isbn
9783319109268
Lccn
2014948344
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)886485419
Label
Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 159-171) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- Part 1. Metric Spaces -- Introduction -- Caristi's Theorem and Extensions -- Nonexpansive Mappings and Zermelo's Theorem -- Hyperconvex metric spaces -- Ultrametric spaces -- Part 2. Length Spaces and Geodesic Spaces -- Busemann spaces and hyperbolic spaces -- Length spaces and local contractions -- The G-spaces of Busemann -- CAT(0) Spaces -- Ptolemaic Spaces -- R-Trees (metric trees) -- Part 3. Beyond Metric Spaces -- b-Metric Spaces -- Generalized Metric Spaces -- Partial Metric Spaces -- Diversities -- Bibliography -- Index
Control code
903490019
Dimensions
24 cm
Extent
xi, 173 pages
Isbn
9783319109268
Lccn
2014948344
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)886485419

Library Locations

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      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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