Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectivel...

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Autores: Som, Sumit, Gabeleh, Moosa, De la Sen Parte, Manuel
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/57882
Acceso en línea:http://hdl.handle.net/10810/57882
Access Level:acceso abierto
Palabra clave:best proximity point
F-proximal contraction
F-contraction of Hardy-Rogers-type
generalized F-proximal contraction of the first kind
generalized F-proximal contraction of the second kind
Geraghty contraction
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spelling Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal ContractionsSom, SumitGabeleh, MoosaDe la Sen Parte, Manuelbest proximity pointF-proximal contractionF-contraction of Hardy-Rogers-typegeneralized F-proximal contraction of the first kindgeneralized F-proximal contraction of the second kindGeraghty contractionIn the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems.This research was funded by Basque Government (Grant No. 1207-19).MDPI2022202220222022info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/57882reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://www.mdpi.com/2075-1680/11/9/468info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/© 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).oai:addi.ehu.eus:10810/578822026-06-18T09:23:17Z
dc.title.none.fl_str_mv Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
title Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
spellingShingle Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
Som, Sumit
best proximity point
F-proximal contraction
F-contraction of Hardy-Rogers-type
generalized F-proximal contraction of the first kind
generalized F-proximal contraction of the second kind
Geraghty contraction
title_short Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
title_full Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
title_fullStr Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
title_full_unstemmed Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
title_sort Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions
dc.creator.none.fl_str_mv Som, Sumit
Gabeleh, Moosa
De la Sen Parte, Manuel
author Som, Sumit
author_facet Som, Sumit
Gabeleh, Moosa
De la Sen Parte, Manuel
author_role author
author2 Gabeleh, Moosa
De la Sen Parte, Manuel
author2_role author
author
dc.subject.none.fl_str_mv best proximity point
F-proximal contraction
F-contraction of Hardy-Rogers-type
generalized F-proximal contraction of the first kind
generalized F-proximal contraction of the second kind
Geraghty contraction
topic best proximity point
F-proximal contraction
F-contraction of Hardy-Rogers-type
generalized F-proximal contraction of the first kind
generalized F-proximal contraction of the second kind
Geraghty contraction
description In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/57882
url http://hdl.handle.net/10810/57882
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.mdpi.com/2075-1680/11/9/468
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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