Right Bregman nonexpansive operators in Banach spaces

We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence w...

Descripción completa

Detalles Bibliográficos
Autores: Martín Márquez, Victoria, Reich, Simeon, Sabach, Shoham
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/47199
Acceso en línea:http://hdl.handle.net/11441/47199
https://doi.org/10.1016/j.na.2012.04.048
Access Level:acceso abierto
Palabra clave:Boltzmann-Shannon entropy
Bregman distance
Bregman firmly nonexpansive operator
Fermi-Dirac entropy
Legendre function
Monotone mapping
Nonexpansive operator
Reflexive Banach space
Resolvent
Retraction
T-monotone mapping
Totally convex function
id ES_44bd4cc69b4fc2e09df211585f6b3576
oai_identifier_str oai:idus.us.es:11441/47199
network_acronym_str ES
network_name_str España
repository_id_str
spelling Right Bregman nonexpansive operators in Banach spacesMartín Márquez, VictoriaReich, SimeonSabach, ShohamBoltzmann-Shannon entropyBregman distanceBregman firmly nonexpansive operatorFermi-Dirac entropyLegendre functionMonotone mappingNonexpansive operatorReflexive Banach spaceResolventRetractionT-monotone mappingTotally convex functionWe introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence we show that the fixed point set of any right quasi-Bregman nonexpansive operator is a sunny right quasi-Bregman nonexpansive retract of the ambient Banach space.Dirección General de Enseñanza SuperiorJunta de AndalucíaIsrael Science FoundationGraduate School of the TechnionFund for the Promotion of Research at the TechnionTechnion VPR FundElsevierAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/47199https://doi.org/10.1016/j.na.2012.04.048reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Analysis: Theory, Methods and Applications, 75 (14), 5448-5465.BFM2009-1096-C02-01FQM-127647/07http://ac.els-cdn.com/S0362546X12001836/1-s2.0-S0362546X12001836-main.pdf?_tid=a1e792dc-8c7e-11e6-8962-00000aacb361&acdnat=1475838799_aef7f227d812375b8f4df5ec2f787e84info:eu-repo/semantics/openAccessoai:idus.us.es:11441/471992026-06-17T12:51:07Z
dc.title.none.fl_str_mv Right Bregman nonexpansive operators in Banach spaces
title Right Bregman nonexpansive operators in Banach spaces
spellingShingle Right Bregman nonexpansive operators in Banach spaces
Martín Márquez, Victoria
Boltzmann-Shannon entropy
Bregman distance
Bregman firmly nonexpansive operator
Fermi-Dirac entropy
Legendre function
Monotone mapping
Nonexpansive operator
Reflexive Banach space
Resolvent
Retraction
T-monotone mapping
Totally convex function
title_short Right Bregman nonexpansive operators in Banach spaces
title_full Right Bregman nonexpansive operators in Banach spaces
title_fullStr Right Bregman nonexpansive operators in Banach spaces
title_full_unstemmed Right Bregman nonexpansive operators in Banach spaces
title_sort Right Bregman nonexpansive operators in Banach spaces
dc.creator.none.fl_str_mv Martín Márquez, Victoria
Reich, Simeon
Sabach, Shoham
author Martín Márquez, Victoria
author_facet Martín Márquez, Victoria
Reich, Simeon
Sabach, Shoham
author_role author
author2 Reich, Simeon
Sabach, Shoham
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Boltzmann-Shannon entropy
Bregman distance
Bregman firmly nonexpansive operator
Fermi-Dirac entropy
Legendre function
Monotone mapping
Nonexpansive operator
Reflexive Banach space
Resolvent
Retraction
T-monotone mapping
Totally convex function
topic Boltzmann-Shannon entropy
Bregman distance
Bregman firmly nonexpansive operator
Fermi-Dirac entropy
Legendre function
Monotone mapping
Nonexpansive operator
Reflexive Banach space
Resolvent
Retraction
T-monotone mapping
Totally convex function
description We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence we show that the fixed point set of any right quasi-Bregman nonexpansive operator is a sunny right quasi-Bregman nonexpansive retract of the ambient Banach space.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/47199
https://doi.org/10.1016/j.na.2012.04.048
url http://hdl.handle.net/11441/47199
https://doi.org/10.1016/j.na.2012.04.048
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Analysis: Theory, Methods and Applications, 75 (14), 5448-5465.
BFM2009-1096-C02-01
FQM-127
647/07
http://ac.els-cdn.com/S0362546X12001836/1-s2.0-S0362546X12001836-main.pdf?_tid=a1e792dc-8c7e-11e6-8962-00000aacb361&acdnat=1475838799_aef7f227d812375b8f4df5ec2f787e84
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407114402725888
score 15,300719

Similares en LA Referencia