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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}i=1,n=1m,∞ 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.

Approximating fixed points for a reversible semigroup of Lipschitzian mappings in a smooth Banach space