A new class of \(\mathcal{S}\)-contractions in complete metric spaces and \(\mathcal{G_{P}}\)-contractions in ordered metric spaces
type: Item
instance of: scholarly article
title: A new class of \(\mathcal{S}\)-contractions in complete metric spaces and \(\mathcal{G_{P}}\)-contractions in ordered metric spaces
zbMATH Open document ID: 1356.54045
author: Somayya Komal
author: Poom Kumam
published in: Fixed Point Theory and Applications
publication date: 2016-08-09T00:00:00Z
review text: The authors introduce the notions of \(S\)-contractions and \({\mathcal G}_P\)-contractions and prove the following results. Let \(A\), \(B\) be nonempty closed subsets of \(X\). If \(S,T: A\to B\) are \(S\)-contractions satisfying some conditions in a complete metric space \((X,d)\), then there exists a unique common best proximity point \(x\in A\) such that \(d(x, Tx)= d(A, B)= d(x, Sx)\). If \(f: A\to B\) is a \({\mathcal G}_P\)-contraction satisfying some conditions in a complete partially ordered metric space \((X,\preccurlyeq, d)\), then there exists a unique point \(x\in A\) such that \(d(x,fx)= d(A,B)\).
reviewed by: Jarosław Górnicki
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6610397
zbMATH Keywords: common best proximity point
zbMATH Keywords: common fixed point
zbMATH Keywords: best proximity point
zbMATH Keywords: fixed point
zbMATH Keywords: \(\mathcal{S}\)-contraction
zbMATH Keywords: \(\mathcal{G_{P}}\)-function
zbMATH Keywords: \(\mathcal{G_{P}}\)-contraction
zbMATH Keywords: proximally commuting mappings
zbMATH Keywords: \(P\)-property
MaRDI profile type: Publication
full work available at URL: s13663-016-0556-x
OpenAlex ID: W2503987298
Wikidata QID: Q59306860
cites work: Extensions of Banach's Contraction Principle
cites work: Extensions of two fixed point theorems of F. E. Browder
cites work: Best proximity points: Global optimal approximate solutions
cites work: Best proximity point theorems generalizing the contraction principle
cites work: Best proximity points: approximation and optimization
cites work: Common best proximity points: global minimization of multi-objective functions
cites work: Common best proximity points: global minimal solutions
cites work: A coincidence best proximity point problem in \(G\)-metric spaces
cites work: Global optimal solutions of noncyclic mappings in metric spaces
cites work: Coupled best proximity point theorem in metric spaces
cites work: On \(\mathcal P\)-contractions in ordered metric spaces
DOI: 10.1186/S13663-016-0556-X
Recommended article: A new class of generalized contraction using \(\mathcal P\)-functions in ordered metric spaces
Recommended article: On \(\mathcal P\)-contractions in ordered metric spaces
Recommended article: Fixed point results for ordered S-G-contractions in ordered metric spaces
Recommended article: New contractive conditions of integral type on complete \(S\)-metric spaces
Recommended article: Generalized $F$-contractions in Partially Ordered Metric Spaces
Recommended article: A new class of contraction in \(b\)-metric spaces and applications
Recommended article: On generalized weakly \(G\)-contractive mappings in partially ordered \(G\)-metric spaces
Recommended article: Some new contractive mappings on \(S\)-metric spaces and their relationships with the mapping (S25)
Recommended article: On generalized weakly \(GP\)-contractive mappings in ordered \(GP\)-metric spaces
Recommended article: Q3191420
description: scientific article; zbMATH DE number 6610397