The Stability of Solution Set to η-Set-Valued Weak Vector Variational Inequality Problem

In this paper, we discuss the upper semi-continuity of the solution to parameterη-Set-valued weak vector variational inequality problem. We show that the operator of parameterη-Set-valued weak vector variational inequality is not continuous, but it satisfiesν-semicontinuous andη-weakCpseudo-monotone. Our results generalize the previous results in the literature.

Existence theorems for vector variational inequalities

Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.