On the Generalized Nonlinear Variational Inequalities and Quasi-Variational Inequalities

The purpose of this paper is to investigate the existence of solutions for a class of generalized nonlinear inequalities GNVI.and generalized nonlinear quasi- variational inequalities GNQVI.with non-monotone set-valued operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. Results that generalize and unify corresponding recent results of Ding and Tarafdar are derived.