We introduce an iterative method for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real valued functions of the semigroup. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Compared to the similar works, our results have the merit of imposing weaker hypotheses on coefficients
