A note on Chan and Pangʹs existence theorem for generalized quasi-variational inequalities Original Research Article

In this note, we deal with the following problem: given a nonempty closed convex subset X of Rn and two multifunctions Γ : X → 2X, Φ : X → 2Rn, find View the MathML source such that View the MathML source We prove that if each Γ(x) has nonempty interior, then the upper semicontinuity and closed-valuedness assumption on the multifunction Γ in the classical Chan and Pangʹs existence result can be weakened to the following: the set {x ∈ X : x ∈ Γ(x)} is closed.