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 setvalued 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
 1 online resource (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 Gspaces of Busemann
 CAT(0) Spaces
 Ptolemaic Spaces
 Rtrees (metric trees)
 Part 3. Beyond Metric Spaces
 bMetric Spaces
 Generalized Metric Spaces
 Partial Metric Spaces
 Diversities
 Bibliography
 Index
 Isbn
 9783319364056
 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 setvalued 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
 N$T
 http://library.link/vocab/creatorName
 Kirk, W. A
 Dewey number
 514/.3
 Index
 index present
 LC call number
 QA329.9
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Shahzad, Naseer
 http://library.link/vocab/subjectName

 Fixed point theory
 Topology
 Mathematics
 Differential Geometry
 Topology
 Mathematical Modeling and Industrial Mathematics
 MATHEMATICS
 Fixed point theory
 Topology
 Label
 Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 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 Gspaces of Busemann  CAT(0) Spaces  Ptolemaic Spaces  Rtrees (metric trees)  Part 3. Beyond Metric Spaces  bMetric Spaces  Generalized Metric Spaces  Partial Metric Spaces  Diversities  Bibliography  Index
 Control code
 894508979
 Dimensions
 unknown
 Extent
 1 online resource (xi, 173 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319364056
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319109275
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)894508979
 Label
 Fixed point theory in distance spaces, William Kirk, Naseer Shahzad
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 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 Gspaces of Busemann  CAT(0) Spaces  Ptolemaic Spaces  Rtrees (metric trees)  Part 3. Beyond Metric Spaces  bMetric Spaces  Generalized Metric Spaces  Partial Metric Spaces  Diversities  Bibliography  Index
 Control code
 894508979
 Dimensions
 unknown
 Extent
 1 online resource (xi, 173 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319364056
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319109275
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)894508979
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