Let

$K$ be a closed convex subset of a real Hilbert space

$H$,

$A:K\to H$ be inverse strongly monotone, and

$S:K\to K$ be nonexpansive. Assuming that the set of solutions of the variational inequality for

$A$ and the set of fixed points of

$S$ have a nonempty intersection, the authors introduce an iteration process that is shown to generate a sequence converging weakly to an element of this intersection. This is the main result of the paper, which is then applied to obtain a sequence converging to a common fixed point of a nonexpansive map and a strictly pseudocontractive map.