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.