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Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds
This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibriu...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5424001/ https://www.ncbi.nlm.nih.gov/pubmed/28553057 http://dx.doi.org/10.1186/s13660-017-1375-2 |
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author | Lu, Haishu Wang, Zhihua |
author_facet | Lu, Haishu Wang, Zhihua |
author_sort | Lu, Haishu |
collection | PubMed |
description | This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbed saddle point problem. Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities. The results presented in this paper unify and generalize many known results in the literature. |
format | Online Article Text |
id | pubmed-5424001 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-54240012017-05-25 Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds Lu, Haishu Wang, Zhihua J Inequal Appl Research This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbed saddle point problem. Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities. The results presented in this paper unify and generalize many known results in the literature. Springer International Publishing 2017-05-10 2017 /pmc/articles/PMC5424001/ /pubmed/28553057 http://dx.doi.org/10.1186/s13660-017-1375-2 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Lu, Haishu Wang, Zhihua Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title | Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title_full | Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title_fullStr | Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title_full_unstemmed | Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title_short | Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds |
title_sort | abstract generalized vector quasi-equilibrium problems in noncompact hadamard manifolds |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5424001/ https://www.ncbi.nlm.nih.gov/pubmed/28553057 http://dx.doi.org/10.1186/s13660-017-1375-2 |
work_keys_str_mv | AT luhaishu abstractgeneralizedvectorquasiequilibriumproblemsinnoncompacthadamardmanifolds AT wangzhihua abstractgeneralizedvectorquasiequilibriumproblemsinnoncompacthadamardmanifolds |