The canonical partial metric and the uniform convexity on normed spaces

[EN] In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove th...

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Detalles Bibliográficos
Autores: Oltra, S., Romaguera, Salvador, Sánchez-Pérez, E.A.
Tipo de recurso: artículo
Fecha de publicación:2005
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:10251/82633
Acceso en línea:https://riunet.upv.es/handle/10251/82633
Access Level:acceso abierto
Palabra clave:Partial metric
Convexity
Normed spaces
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spelling The canonical partial metric and the uniform convexity on normed spacesOltra, S.Romaguera, SalvadorSánchez-Pérez, E.A.Partial metricConvexityNormed spaces[EN] In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.The authors acknowledge the support of the Generalidad Valenciana, grant GV04B-371, the Spanish Ministry of Science and Technology, Plan Nacional I+D+I, grant BFM2003-02302, and FEDER, and the Polytechnical University of Valencia.Universitat Politècnica de ValènciaGeneralitat ValencianaMinisterio de Ciencia y TecnologíaUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20052005-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/82633reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 GV 04B-371Ministerio de Ciencia y Tecnología https://doi.org/10.13039/501100006280 BFM2003-02302open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/826332026-06-13T07:49:27Z
dc.title.none.fl_str_mv The canonical partial metric and the uniform convexity on normed spaces
title The canonical partial metric and the uniform convexity on normed spaces
spellingShingle The canonical partial metric and the uniform convexity on normed spaces
Oltra, S.
Partial metric
Convexity
Normed spaces
title_short The canonical partial metric and the uniform convexity on normed spaces
title_full The canonical partial metric and the uniform convexity on normed spaces
title_fullStr The canonical partial metric and the uniform convexity on normed spaces
title_full_unstemmed The canonical partial metric and the uniform convexity on normed spaces
title_sort The canonical partial metric and the uniform convexity on normed spaces
dc.creator.none.fl_str_mv Oltra, S.
Romaguera, Salvador
Sánchez-Pérez, E.A.
author Oltra, S.
author_facet Oltra, S.
Romaguera, Salvador
Sánchez-Pérez, E.A.
author_role author
author2 Romaguera, Salvador
Sánchez-Pérez, E.A.
author2_role author
author
dc.contributor.none.fl_str_mv Generalitat Valenciana
Ministerio de Ciencia y Tecnología
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Partial metric
Convexity
Normed spaces
topic Partial metric
Convexity
Normed spaces
description [EN] In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.
publishDate 2005
dc.date.none.fl_str_mv 2005
2005-10-01
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/10251/82633
url https://riunet.upv.es/handle/10251/82633
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 GV 04B-371
Ministerio de Ciencia y Tecnología https://doi.org/10.13039/501100006280 BFM2003-02302
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/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 - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
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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