A minimax inequality and its applications to variational inequalities

In this paper we get a slight generalization of a Ky Fan’s result which concerns with a minimax inequality. We shall use this result to give a direct proof for the existence of solutions of the following two variational inequalities where T⊂zE×E’ is monotone, E is a reflexive Banach space with its dual E’ X is a closed convex bounded subset of E, and h is a lower semicontinuous convex function from X into R.