A kind of system of multivariate variational inequalities and the existence theorem of solutions

Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see...

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Autores principales: Tang, Yanxia, Guan, Jinyu, Xu, Yongchun, Su, Yongfu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5589815/
https://www.ncbi.nlm.nih.gov/pubmed/28943738
http://dx.doi.org/10.1186/s13660-017-1486-9
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author Tang, Yanxia
Guan, Jinyu
Xu, Yongchun
Su, Yongfu
author_facet Tang, Yanxia
Guan, Jinyu
Xu, Yongchun
Su, Yongfu
author_sort Tang, Yanxia
collection PubMed
description Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see text] ; (2) the set of solutions of this system of multivariate variational inequalities is closed convex in [Formula: see text] ; (3) if [Formula: see text] are also strictly monotone, this system of multivariate variational inequalities has a unique solution.
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spelling pubmed-55898152017-09-22 A kind of system of multivariate variational inequalities and the existence theorem of solutions Tang, Yanxia Guan, Jinyu Xu, Yongchun Su, Yongfu J Inequal Appl Research Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see text] ; (2) the set of solutions of this system of multivariate variational inequalities is closed convex in [Formula: see text] ; (3) if [Formula: see text] are also strictly monotone, this system of multivariate variational inequalities has a unique solution. Springer International Publishing 2017-09-07 2017 /pmc/articles/PMC5589815/ /pubmed/28943738 http://dx.doi.org/10.1186/s13660-017-1486-9 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
Tang, Yanxia
Guan, Jinyu
Xu, Yongchun
Su, Yongfu
A kind of system of multivariate variational inequalities and the existence theorem of solutions
title A kind of system of multivariate variational inequalities and the existence theorem of solutions
title_full A kind of system of multivariate variational inequalities and the existence theorem of solutions
title_fullStr A kind of system of multivariate variational inequalities and the existence theorem of solutions
title_full_unstemmed A kind of system of multivariate variational inequalities and the existence theorem of solutions
title_short A kind of system of multivariate variational inequalities and the existence theorem of solutions
title_sort kind of system of multivariate variational inequalities and the existence theorem of solutions
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5589815/
https://www.ncbi.nlm.nih.gov/pubmed/28943738
http://dx.doi.org/10.1186/s13660-017-1486-9
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