Pointwise eventually non-expansive action of semi-topological semigroups and fixed points

In this paper we define pointwise eventually non-expansive action of semi-topological semigroups and prove fixed point theorems for it. As a result we give an affirmative answer (without any extra condition on the Banach space) to an open problem raised by Kirk and Xu (2008) [7]. Our results also extend and improve fixed point theorems of Lim and Lau–Mah.