Hi!

Let $\displaystyle G \in \mathbb{C}$ be a bounded domain and let $\displaystyle f_n$ be a sequence of functions that are holomorphic on $\displaystyle G$ and continuous on $\displaystyle \overline{G}$. Show that if $\displaystyle f_n$ converges uniformly on $\displaystyle \partial G$, then it converges uniformly on $\displaystyle \overline{G}$ as well.

I think one has to use Montel's theorem, but I dont know...