Viscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process {x n }, where x 0 ∈ C is arbitrary and x n+1 = α n f (x n ) + (1 − α n )SP C (x n − λ n Ax n ), f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H . It is shown that {x n } converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

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