FINITE-DIMENSIONAL QUASI-VARIATIONAL INEQUALITIES ASSOCIATED WITH DISCONTINUOUS FUNCTIONS

In this paper, given a nonempty closed convex set X subset-of-or-equal-to R(n), a function f: X --> R(n), and a multifunction GAMMA: X --> 2X, we deal with the problem of finding a point x triple-overdot is-an-element-of X such that x triple-overdot is-an-element-of GAMMA(x triple-overdot) and < f (x triple-overdot), x triple-overdot - y> less-than-or-equal-to 0, for all y is-an-element-of GAMMA(x triple-overdot). For such problem, we establish a result where, in particular, the function f is not assumed to be continuous. More precisely, we extend to the present setting a finite-dimensional version of a result by Ricceri on variational inequalities (Ref. 1).