We use the CQ method for approximating a common fixed
point of a left amenable semigroup of nonexpansive mappings, an infinite family of strictly pseudo-contraction mappings and the set of solutions of variational inequalities for monotone, Lipschitz-continuous mappings in a real Hilbert space. Our results are a generalization of a result
announced by Nadezhkina and Takahashi [N. Nadezhkina and W. Takahashi, Strong convergence theorem by a hybrid method for nonexpansive
mappings and Lipschitz-continuous monotone mappings, SIAM J. Optim.
16 (2006), 1230–1241] and some other recent results.