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Let  Open image in new window  be a left amenable semigroup, let  Open image in new window  be a representation of  Open image in new window  as Lipschitzian mappings from a nonempty compact convex subset  Open image in new window  of a smooth Banach space E into C with a uniform Lipschitzian condition, let  Open image in new window  be a strongly left regular sequence of means defined on an  Open image in new window -stable subspace of  Open image in new window , let  Open image in new window  be a contraction on  Open image in new window , and let  Open image in new window  be sequences in (0, 1) such that  Open image in new window , for all n. Let  Open image in new window , for all  Open image in new window . Then, under suitable hypotheses on the constants, we show that  Open image in new window  converges strongly to some  Open image in new window  in  Open image in new window , the set of common fixed points of  Open image in new window , which is the unique solution of the variational inequality  Open image in new window , for all  Open image in new window .

Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces