Generalized metric spaces: a survey
type: Item
instance of: scholarly article
title: Generalized metric spaces: a survey
zbMATH Open document ID: 1331.54031
published in: Journal of Fixed Point Theory and Applications
publication date: 2015-11-09T00:00:00Z
review text: This expository article gives a survey of the following generalizations of metric spaces: pseudometric spaces, quasi-metric spaces, semimetric spaces, metric spaces over graphs, \(b\)-metric spaces, vector-valued metric, in particular, cone metric spaces, 2-metric spaces, \(G\)-metric spaces, partially ordered metric spaces, modular and pseudomodular metric spaces. Several examples and comments concerning the usage of these classes of spaces, in particular in fixed point results, are presented, together with refinements of some known results.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54-02
zbMATH DE Number: 6506114
zbMATH Keywords: Banach contraction principle
zbMATH Keywords: fixed point
zbMATH Keywords: cone metric space
zbMATH Keywords: generalized metric space
zbMATH Keywords: Menger space
zbMATH Keywords: \(b\)-metric space
zbMATH Keywords: \(G\)-metric space
zbMATH Keywords: modular metric space
zbMATH Keywords: ordered metric space
author: M. A. Khamsi
MaRDI profile type: Publication
full work available at URL: s11784-015-0232-5
OpenAlex ID: W4379279608
cites work: Fixed point results of pointwise contractions in modular metric spaces
cites work: On the fixed points of nonexpansive mappings in modular metric spaces
cites work: Contraction and approximate contraction with an application to multi- point boundary value problems
cites work: Extension of uniformly continuous transformations and hyperconvex metric spaces
cites work: Categorial characterization of the MacNeille completion
cites work: An introduction to nonlinear boundary value problems
cites work: Modular metric spaces. I: Basic concepts
cites work: Modular metric spaces. II: Application to superposition operators
cites work: Multi-valued contraction mappings in generalized metric spaces
cites work: Q4225413
cites work: Comment on `Fixed point theorems for contraction mappings in modular metric spaces'
cites work: Q5286518
cites work: Q3148640
cites work: Q4840284
cites work: Q4846632
cites work: Q3148558
cites work: Q4538829
cites work: A note on cone metric fixed point theory and its equivalence
cites work: Synthetic topology: of data types and classical spaces
cites work: Metric Methods Three Examples and a Theorem
cites work: Fixpoint semantics for logic programming a survey
cites work: 2‐metrische Räume und ihre topologische Struktur
cites work: Q3796207
cites work: The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
cites work: Q4693180
cites work: Cone metric spaces and fixed point theorems of contractive mappings
cites work: On cone metric spaces: a survey
cites work: Q3730636
cites work: A note on the equivalence of some metric and cone metric fixed point results
cites work: Remarks on cone metric spaces and fixed point theorems of contractive mappings
cites work: An Introduction to Metric Spaces and Fixed Point Theory
cites work: Fixed point theory in modular function spaces
cites work: The method of successive approximations for functional equations
cites work: Fixed Point Theory in Distance Spaces
cites work: Q3994746
cites work: Q3807603
cites work: Q4551182
cites work: Partial Metric Topology
cites work: Fixed point theorems for contraction mappings in modular metric spaces
cites work: Orlicz spaces and modular spaces
cites work: Q5465199
cites work: Q3410667
cites work: Fixed point theorems for contractive mappings in complete \(G\)-metric spaces
cites work: Q5801558
cites work: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations
cites work: Q3994502
cites work: Q5533445
cites work: A fixed point theorem in partially ordered sets and some applications to matrix equations
cites work: Zone and double zone diagrams in abstract spaces
cites work: Q5663096
cites work: Electrorheological fluids: modeling and mathematical theory
cites work: Q3940355
cites work: On nonlinear contraction semigroups in sup norm spaces
cites work: Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
cites work: Q4167271

Generalized metric spaces: a survey (cites work)
cites work: A lattice-theoretical fixpoint theorem and its applications

Generalized metric spaces: a survey (cites work)
cites work: Q5553429

Generalized metric spaces: a survey (DOI)
DOI: 10.1007/S11784-015-0232-5