In this paper, we approximate a fixed point of the semigroup ϕ = {Ts : s ∈ S} of Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition and with respect to a finite family of sequences {μi,n} m, ∞ i=1,n=1 of left strong regular invariant means defined on an appropriate invariant subspace of l ∞(S). Our result extends the main results announced by several others.
