Let be a nonempty closed convex and bounded subset of a reflexive Banach space . Let [Formula: see text] be -variables monotone demi-continuous mappings from [Formula: see text] into . 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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| http://dx.doi.org/10.1186/s13660-017-1486-9 | DOI Listing |
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