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:
(1)
and
(2)
where T ⊂ E ×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.
