In this paper, we prove the following theorem: Let $C$ be a nonempty
closed convex subset of a uniformly convex Banach space $E$ whose norm
is uniformly G\^ateaux differentiable, let $\Im=\{T(t):t\geq 0\}$ be a
strongly continuous semigroup of nonexpansive mappings on $C$ such that
$F(\Im)=\bigcap_{t\geq 0}F(T(t))\neq \emptyset$ and let $P$ be the sunny
nonexpansive retraction from $C$ onto $F(\Im)$. For some $u\in C$,
define a sequence $\{x_{n}\}$ in $C$ by
$x_{n}=(1-\alpha_{n})T(t_{n})x_{n}+\alpha_{n}u$, where $0<\alpha_{n}<1$,
$t_{n}>0$ for all $n\geq 1$ and $\displaystyle\lim_{n\to
\infty}t_{n}=\displaystyle\lim_{n\to
\infty}\frac{\alpha_{n}}{t_{n}}=0$. Then $\{x_{n}\}$ converges strongly
to $Pu$.