On Modular b-Metrics

[EN] The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach...

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Autor: Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/211941
Acceso en línea:https://riunet.upv.es/handle/10251/211941
Access Level:acceso abierto
Palabra clave:Modular b-metric
Uniformity
Metrizable
Complete
Modular b-Caristi mapping
Caristi-Kirk s theorem
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spelling On Modular b-MetricsRomaguera Bonilla, Salvador|||0000-0001-7857-6139Modular b-metricUniformityMetrizableCompleteModular b-Caristi mappingCaristi-Kirk s theorem[EN] The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach's contraction principle for this new class of spaces thus initiating the study of the fixed point theory for these structures, where other authors have also made extensive contributions. In this paper we endow the modular b-metrics with a metrizable topology that supplies a firm endorsement of the idea of convergence proposed by Ege and Alaca in their article. Moreover, for a large class of modular b-metric spaces, we formulate this topology in terms of an explicitly defined b-metric, which extends both an important metrization theorem due to Chistyakov as well as the so-called topology of metric convergence. This approach allows us to characterize the completeness for this class of modular b-metric spaces that may be viewed as an offsetting of the celebrated Caristi-Kirk theorem to our context. We also include some examples that endorse our results.MDPI AGInstituto Universitario de Matemática Pura y AplicadaRepositorio Institucional de la Universitat Politècnica de València Riunet20242024-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/211941reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2119412026-06-13T07:49:27Z
dc.title.none.fl_str_mv On Modular b-Metrics
title On Modular b-Metrics
spellingShingle On Modular b-Metrics
Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Modular b-metric
Uniformity
Metrizable
Complete
Modular b-Caristi mapping
Caristi-Kirk s theorem
title_short On Modular b-Metrics
title_full On Modular b-Metrics
title_fullStr On Modular b-Metrics
title_full_unstemmed On Modular b-Metrics
title_sort On Modular b-Metrics
dc.creator.none.fl_str_mv Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author_facet Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author_role author
dc.contributor.none.fl_str_mv Instituto Universitario de Matemática Pura y Aplicada
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Modular b-metric
Uniformity
Metrizable
Complete
Modular b-Caristi mapping
Caristi-Kirk s theorem
topic Modular b-metric
Uniformity
Metrizable
Complete
Modular b-Caristi mapping
Caristi-Kirk s theorem
description [EN] The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach's contraction principle for this new class of spaces thus initiating the study of the fixed point theory for these structures, where other authors have also made extensive contributions. In this paper we endow the modular b-metrics with a metrizable topology that supplies a firm endorsement of the idea of convergence proposed by Ege and Alaca in their article. Moreover, for a large class of modular b-metric spaces, we formulate this topology in terms of an explicitly defined b-metric, which extends both an important metrization theorem due to Chistyakov as well as the so-called topology of metric convergence. This approach allows us to characterize the completeness for this class of modular b-metric spaces that may be viewed as an offsetting of the celebrated Caristi-Kirk theorem to our context. We also include some examples that endorse our results.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/211941
url https://riunet.upv.es/handle/10251/211941
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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