Equilibrium problems on Riemannian manifolds with applications

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and...

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Autores: Wang, Xiangmei, López Acedo, Genaro, Li, Chong, Yao, Jen-Chih
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/83899
Acceso en línea:https://hdl.handle.net/11441/83899
https://doi.org/10.1016/j.jmaa.2018.12.073
Access Level:acceso abierto
Palabra clave:Riemannian manifold
Equilibrium problem
Variational inequality problem
Proximal point algorithm
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spelling Equilibrium problems on Riemannian manifolds with applicationsWang, XiangmeiLópez Acedo, GenaroLi, ChongYao, Jen-ChihRiemannian manifoldEquilibrium problemVariational inequality problemProximal point algorithmWe study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.National Natural Science Foundation of ChinaNatural Science Foundation of Guizhou Province (China)Dirección General de Enseñanza SuperiorJunta de AndalucíaNational Science Council of TaiwanElsevierAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/83899https://doi.org/10.1016/j.jmaa.2018.12.073reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Analysis and Applications, 473 (2), 866-891.115713081166101920161039MTM2015-65242-C2-1PFQM-127102-2115-M-039-003-MY3https://reader.elsevier.com/reader/sd/pii/S0022247X19300149?token=085B15BCEE21C67C8E00175773970A21D820A2FC2BA21EEF2C990447EBC869D4A1F8B98A435E2FC60EEAF00917A60C16info:eu-repo/semantics/openAccessoai:idus.us.es:11441/838992026-06-17T12:51:07Z
dc.title.none.fl_str_mv Equilibrium problems on Riemannian manifolds with applications
title Equilibrium problems on Riemannian manifolds with applications
spellingShingle Equilibrium problems on Riemannian manifolds with applications
Wang, Xiangmei
Riemannian manifold
Equilibrium problem
Variational inequality problem
Proximal point algorithm
title_short Equilibrium problems on Riemannian manifolds with applications
title_full Equilibrium problems on Riemannian manifolds with applications
title_fullStr Equilibrium problems on Riemannian manifolds with applications
title_full_unstemmed Equilibrium problems on Riemannian manifolds with applications
title_sort Equilibrium problems on Riemannian manifolds with applications
dc.creator.none.fl_str_mv Wang, Xiangmei
López Acedo, Genaro
Li, Chong
Yao, Jen-Chih
author Wang, Xiangmei
author_facet Wang, Xiangmei
López Acedo, Genaro
Li, Chong
Yao, Jen-Chih
author_role author
author2 López Acedo, Genaro
Li, Chong
Yao, Jen-Chih
author2_role author
author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Riemannian manifold
Equilibrium problem
Variational inequality problem
Proximal point algorithm
topic Riemannian manifold
Equilibrium problem
Variational inequality problem
Proximal point algorithm
description We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.
publishDate 2019
dc.date.none.fl_str_mv 2019
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 https://hdl.handle.net/11441/83899
https://doi.org/10.1016/j.jmaa.2018.12.073
url https://hdl.handle.net/11441/83899
https://doi.org/10.1016/j.jmaa.2018.12.073
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Mathematical Analysis and Applications, 473 (2), 866-891.
11571308
11661019
20161039
MTM2015-65242-C2-1P
FQM-127
102-2115-M-039-003-MY3
https://reader.elsevier.com/reader/sd/pii/S0022247X19300149?token=085B15BCEE21C67C8E00175773970A21D820A2FC2BA21EEF2C990447EBC869D4A1F8B98A435E2FC60EEAF00917A60C16
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
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score 15,300719

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