Semi-asymptotic non-expansive action of amenable semigroups and fixed points

We present in this paper a common fixed point property for a semi-topological semigroup of semi-asymptotically non-expansive mappings acting on a weakly compact convex subset K of a Banach space, assuming that certain subspace of B(S) has a left invariant mean. This also extend and improve fixed point theorems of Lau and Lim.