Existence Theorem for Vector Quasi-Variational-like Inequalities

In this paper, using the maximal element theorem, we prove some existence theorem for vector quasi-variational-like inequalities without monotonicity and without compactness. Keywords: Set-valued mapping; vector quasi-variational-like inequality; , maximal element theorem; locally convex Hausdorff topological space; upper semi-continuous; open lower sections; -diagonally convex.