An Application of a Browder-Type Fixed Point Theorem to Generalized Variational Inequalities

The purpose of this paper is to provide an application of a non-compact version, due to Park, of Browder’s fixed point theorem to generalized variational inequalities. In a non-compact setting, we establish a fairly general existence theorem on a generalized variational inequality using the result of Park. Our main result is not only a strict generalization of Ding and Tan’s result without assuming any continuity of given functions, but also a purely infinite dimensional version of recent results of Yao and Guo. As an immediate consequence, we obtain an extension of a result of Browder concerned with generalized variational inequalities without assuming the local convexity of the underlying topological vector space