ON THE SOLUTION EXISTENCE OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS WITH DISCONTINUOUS MULTIFUNCTIONS

In this paper we deal with the following generalized vector quasi-equilibrium 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-n. Let Gamma : K -> 2(K), Phi : K -> 2(D) be two multifunctions and f : K x D x K -> R-n be a single-valued mapping. Find a point (x, y) is an element of K x D such that (x, y) is an element of Gamma(x) x Phi(x) and {f (x, y, z) : z is an element of Gamma(x)} boolean AND (-IntC) = circle divide. We prove some existence theorems for the problem in which Phi can be discontinuous and K can be unbounded.