# Math Help - Analytic Function in the Unit Disk

1. ## Analytic Function in the Unit Disk

Dear Colleagues,

Let $f$ be analytic function in the unit disk $D=\{z \in C:|z|<1\}$ with $|f(z)|<1$, for any $z \in D$. If $f(z_{1})=z_{1}, f(z_{2})=z_{2}$ where $z_{1}$ and $z_{2}$ are distinct, show that $f(z)=z$ for any $z \in D$.