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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Detalles Bibliográficos
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
Descripción
Sumario: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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