On the Solution Existence of Generalized Vector Quasi-equilibrium Problems with Discontinuous Multifunctions

In this paper we deal with the following generalized vector quasiequilibrium problem: given a closed convex set K in a normed space X, a subset D in a Hausdorff topological vector space Y , and a closed convex cone C in R. Let Γ : K → 2, Φ : K → 2 be two multifunctions and f : K×D×K → R be a single-valued mapping. Find a point (x̂, ŷ) ∈ K×D such that (x̂, ŷ) ∈ Γ(x̂)× Φ(x̂), and {f(x̂, ŷ, z) : z ∈ Γ(x̂)} ∩ (−IntC) = Ø. We prove some existence theorems for the problem in which Φ can be discontinuous and K can be unbounded.