Generalized Vector Variational Inequalities with Star-pseudomonotone and Discontinuous Operators

In this paper we deal with the following generalized vector variational inequality problem: let X, Y and Z be topological vector spaces, K be a convex set in X, D be a nonempty set in Y , and C be a closed convex cone in Z. Let T : K → 2 be a multifunction and f : K ×D ×K → Z be a single-valued mapping. Find a point x̂ ∈ K and ŷ ∈ T (x̂) such that f(x̂, ŷ, z) / ∈ −intC, ∀z ∈ K. We prove some existence theorems in which T can be discontinuous, or K can be unbounded, and a existence theorem in which T is pseudomonotone.