$f$ be a holomorphic on a bounded domain $D$ with fixed point $z_0$. Could any one give a hint how to show the following:
$f$ is bijective iff $|f'(z_0)|=1$.
Well, I was thinking like to compose $f,f^2,\dots,f^n$ and apply some how $f^n$ also has $z_0$ as fixed point. Thank you for help.