The Resource Fixed Point Theory in Distance Spaces, by William Kirk, Naseer Shahzad, (electronic resource)

Fixed Point Theory in Distance Spaces, by William Kirk, Naseer Shahzad, (electronic resource)

Label
Fixed Point Theory in Distance Spaces
Title
Fixed Point Theory in Distance Spaces
Statement of responsibility
by William Kirk, Naseer Shahzad
Creator
Contributor
Author
Provider
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
http://library.link/vocab/creatorName
Kirk, William
Image bit depth
0
LC call number
QA641-670
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Shahzad, Naseer.
  • SpringerLink
http://library.link/vocab/subjectName
  • Mathematics
  • Global differential geometry
  • Topology
  • Mathematics
  • Differential Geometry
  • Topology
  • Mathematical Modeling and Industrial Mathematics
Label
Fixed Point Theory in Distance Spaces, by William Kirk, Naseer Shahzad, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XI, 173 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319109275
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-10927-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-10927-5
Label
Fixed Point Theory in Distance Spaces, by William Kirk, Naseer Shahzad, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XI, 173 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319109275
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-10927-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-10927-5

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