GENERALIZED g-QUASIVARIATIONAL INEQUALITY

Suppose that X is a nonempty subset of a metric space E and Y is a nonempty subset of a topological vector space F. Let g: X → Y and ψ: X ×Y →R be two functions and let S: X → 2Y and T: Y → 2F ∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x ∈ X and a point f ∈ T(g(x)) such that g(x) ∈ S(x) and supy∈S(x){Re 〈 f, y − g(x) 〉 + ψ(x, y)} = ψ(x,g(x)). In this paper, we prove the existence of a solution of (GgQVI). 1. Introduction an