We prove that if $S$ is an amenable semigroup and $\varphi= \{T_t: t\in S\}$ is a semigroup of mappings on a nonempty weakly compact, convex subset $C$ of a Banach space $E$, generated by $\{T_t: t\in A\subseteq S\}$, such that for each $t\in A$, $T_t$ is of type $(\gamma)$ and $D(\overline{co} F_{1/n} (T_t),F(T_t))\to 0$, as $n\to\infty$, then $F(\varphi)$ of common fixed points of $\varphi$ is nonempty and there exists a retraction $P$ of type $(\gamma)$ from $C$ onto $F(\varphi)$, such that $PT_t= T_t P= P$ for each $t\in S$, and $Px \in \overline{co}\{ T_t x: t\in S\}$ for each $x\in C$. The compactness of $C$ concludes such imposed conditions.
