The Resource Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
Resource Information
The item Fixed point theory in distance spaces, William Kirk, Naseer Shahzad represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Fixed point theory in distance spaces, William Kirk, Naseer Shahzad represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- xi, 173 pages
- 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
- Isbn
- 9783319109268
- Label
- Fixed point theory in distance spaces
- Title
- Fixed point theory in distance spaces
- Statement of responsibility
- William Kirk, Naseer Shahzad
- 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
- 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
- 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
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