Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups

Let X be a Banach space with a weak uniform normal structure and C a nonempty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t S} of selfmappings on C satisfying liminfSt|T(t)|>WCS(X) has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and |T(t)| is the exact Lipschitz constant of T(t).