Common fixed points in Chebyshev center for a semigroup of isometry mappings

In this article, we prove that if $K$ is a nonempty weakly compact convex set having the normal structure in a Banach space $B$ and $\mathfrak{F}$ is a left reversible semitopological semigroup of isometry mappings from $K$ into itself, then there exists a point in $C(K)$ which is fixed by every member in $\mathfrak{F}$. This gives an affirmative answer to a question raised by Lim et al.