A note on Chan and Pang's existence theorem for generalized quasi-variational inequalities

In this note, we deal with the following problem: given a nonempty closed convex subset X of R(n) and two multifunctions Gamma : X --> 2(X), Phi : X --> 2(Rn), find (x*,x*) is an element of X x R(n) such that x* is an element of Gamma (x*), z* is an element of Phi (x*) and [z*, x* - y] less than or equal to 0 for all y is an element of Gamma (x*). We prove that if each Gamma(x) has nonempty interior, then the upper semicontinuity and closed-valuedness assumption on the multifunction Gamma in the classical Chan and Pang's existence result can be weakened to the following: the set {x is an element of X: x is an element of Gamma(x)} is closed.