A best proximity point result in modular spaces with the Fatou property
type: Item
instance of: scholarly article
title: A best proximity point result in modular spaces with the Fatou property
zbMATH Open document ID: 1325.41019
DOI: 10.1155/2013/329451
author: Mohamed Jleli
author: E. Karapinar
author: Bessem Samet
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: Consider a nonself-mapping \(T:A\to B\), where \((A,B)\) is a pair of nonempty subsets of a modular space \(X_\rho\). A best proximity point of \(T\) is a point \(z\in A\) satisfying the condition: \(\rho(z-Tz)=\mathrm{inf}\{\rho(x-y)\colon(x,y)\in A\times B\}\). In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46A80
zbMATH DE Number: 6306663
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/329451
OpenAlex ID: W2170713844
Wikidata QID: Q58915963
cites work: Q3847669
cites work: Q3954347
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description: scientific article; zbMATH DE number 6306663