On the existence of solutions of variational inequalities in Banach spaces

Abstract

In this paper, we study the existence of the solution of the variational inequality 〈 Tx− ξ, y− x〉⩾0 by applying the generalized projection operator π K :B ∗→B , where B is a Banach space with dual space B ∗ and by using the well-known FanKKM Theorem.