Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence

[EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We...

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Autores: García-Pacheco, Francisco Javier, Kama, Ramazan, Murillo Arcila, Marina
Tipo de recurso: artículo
Fecha de publicación:2022
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:10251/194410
Acceso en línea:https://riunet.upv.es/handle/10251/194410
Access Level:acceso abierto
Palabra clave:Statistical convergence
Uniform convergence
Unconditionally convergent series
Weakly unconditionally Cauchy series
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spelling Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform ConvergenceGarcía-Pacheco, Francisco JavierKama, RamazanMurillo Arcila, MarinaStatistical convergenceUniform convergenceUnconditionally convergent seriesWeakly unconditionally Cauchy series[EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We also obtain generalizations of some results regarding uniform convergence of unconditionally convergent series through the concept of statistical convergence. Finally, we provide a version of the Orlicz- Pettis theorem for A-multiplier convergent operator series by means of the statistical convergence.The first author has been supported by Research Grant PGC-101514-B-I00 awarded by the Ministry of Science, Innovation and Universities of Spain, and by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia, with project reference: FEDER-UCA18-105867. The third author has been supported by MCIN/AEI/10.13039/501100011033, Project PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEU/2021/070.Springer-VerlagJunta de AndalucíaGENERALITAT VALENCIANAAGENCIA ESTATAL DE INVESTIGACIONAgencia Estatal de InvestigaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20222022-02-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/194410reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-101514-B-I00 METODOS ANALITICOS EN SIMETRIAS, TEORIA DE CONTROL Y OPERADORESGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2021%2F070 Análisis funcional, dinámica de operadores y aplicacionesAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105011GB-I00 DINAMICA DE OPERADORESJunta de Andalucía http://dx.doi.org/10.13039/501100011011 FEDER-UCA18-105867open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1944102026-06-13T07:49:27Z
dc.title.none.fl_str_mv Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
title Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
spellingShingle Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
García-Pacheco, Francisco Javier
Statistical convergence
Uniform convergence
Unconditionally convergent series
Weakly unconditionally Cauchy series
title_short Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
title_full Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
title_fullStr Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
title_full_unstemmed Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
title_sort Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence
dc.creator.none.fl_str_mv García-Pacheco, Francisco Javier
Kama, Ramazan
Murillo Arcila, Marina
author García-Pacheco, Francisco Javier
author_facet García-Pacheco, Francisco Javier
Kama, Ramazan
Murillo Arcila, Marina
author_role author
author2 Kama, Ramazan
Murillo Arcila, Marina
author2_role author
author
dc.contributor.none.fl_str_mv Junta de Andalucía
GENERALITAT VALENCIANA
AGENCIA ESTATAL DE INVESTIGACION
Agencia Estatal de Investigación
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Statistical convergence
Uniform convergence
Unconditionally convergent series
Weakly unconditionally Cauchy series
topic Statistical convergence
Uniform convergence
Unconditionally convergent series
Weakly unconditionally Cauchy series
description [EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We also obtain generalizations of some results regarding uniform convergence of unconditionally convergent series through the concept of statistical convergence. Finally, we provide a version of the Orlicz- Pettis theorem for A-multiplier convergent operator series by means of the statistical convergence.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-02-01
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/10251/194410
url https://riunet.upv.es/handle/10251/194410
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-101514-B-I00 METODOS ANALITICOS EN SIMETRIAS, TEORIA DE CONTROL Y OPERADORES
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2021%2F070 Análisis funcional, dinámica de operadores y aplicaciones
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105011GB-I00 DINAMICA DE OPERADORES
Junta de Andalucía http://dx.doi.org/10.13039/501100011011 FEDER-UCA18-105867
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
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 15,300719

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