In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for b-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets.
