Let $S$ be a left amenable semigroup, $\mathcal{S}=\{T(s): s\in S\}$ be a representation of $S$ as Lipschitzian mappings from a nonempty compact convex subset $C$ of a smooth Banach space $E$ into $C$ with a uniform Lipschitzian condition, $\{\mu_n\}$ be a strongly left regular sequence of means defined on an $\mathcal{S}$-stable subspace of $l^{\infty}(S)$, $f$ be a contraction on $C$, and $\{\alpha_n\}$, $\{\beta_n\}$ and $\{\gamma_n\}$ be sequences in $(0,1)$ such that $\alpha_n+\beta_n+\gamma_n=1,$ for all $n.$ Let $x_{n+1}=\alpha_n f(x_n)+\beta_nx_n+\gamma_nT(\mu_n)x_n$, $\forall n\geq 1$. Then, under suitable hypotheses on the constants, we show that $\{x_n\}$ converges strongly to some $z$ in $F(\mathcal{S})$, the set of common fixed points of $\mathcal{S}$, which is the unique solution of the variational inequality $\langle ( f-I)z, J(y-z)\rangle\leq 0, \; \forall y\in F(\mathcal{S}).$
