A mean value theorem for tangentially convex functions

The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously t...

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Detalles Bibliográficos
Autor: Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:275247
Acceso en línea:https://ddd.uab.cat/record/275247
https://dx.doi.org/urn:doi:10.1007/s11228-023-00674-3
Access Level:acceso abierto
Palabra clave:Mean value theorem
Tangential convexity
Tangential subdifferential
Convexity
Monotonicity
Quasiconvexity
Quasimonotonicity
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spelling A mean value theorem for tangentially convex functionsMartínez Legaz, Juan Enrique|||0000-0002-6845-6202Mean value theoremTangential convexityTangential subdifferentialConvexityMonotonicityQuasiconvexityQuasimonotonicityThe main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity. 22023-01-0120232023-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/275247https://dx.doi.org/urn:doi:10.1007/s11228-023-00674-3reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-097960-B-C21Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2019-000915-Sopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2752472026-06-06T12:50:31Z
dc.title.none.fl_str_mv A mean value theorem for tangentially convex functions
title A mean value theorem for tangentially convex functions
spellingShingle A mean value theorem for tangentially convex functions
Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
Mean value theorem
Tangential convexity
Tangential subdifferential
Convexity
Monotonicity
Quasiconvexity
Quasimonotonicity
title_short A mean value theorem for tangentially convex functions
title_full A mean value theorem for tangentially convex functions
title_fullStr A mean value theorem for tangentially convex functions
title_full_unstemmed A mean value theorem for tangentially convex functions
title_sort A mean value theorem for tangentially convex functions
dc.creator.none.fl_str_mv Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
author Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
author_facet Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
author_role author
dc.subject.none.fl_str_mv Mean value theorem
Tangential convexity
Tangential subdifferential
Convexity
Monotonicity
Quasiconvexity
Quasimonotonicity
topic Mean value theorem
Tangential convexity
Tangential subdifferential
Convexity
Monotonicity
Quasiconvexity
Quasimonotonicity
description The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity.
publishDate 2023
dc.date.none.fl_str_mv 2
2023-01-01
2023
2023-01-01
dc.type.none.fl_str_mv 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://ddd.uab.cat/record/275247
https://dx.doi.org/urn:doi:10.1007/s11228-023-00674-3
url https://ddd.uab.cat/record/275247
https://dx.doi.org/urn:doi:10.1007/s11228-023-00674-3
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 https://doi.org/10.13039/501100011033 PGC2018-097960-B-C21
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2019-000915-S
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://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
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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