Analytic Function in the Unit Disk

**raed** · November 8th 2011, 05:01 AM

Dear Colleagues,

Could you please help me in solving the following function:

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 $z \in D$ .

Best Regards,
Raed.

**xxp9** · November 8th 2011, 05:36 AM

Use mobius transform g that maps 0 to z1, then apply Schwarz lemma - Wikipedia, the free encyclopedia to the composed function g^{-1}(f(g))

Thread: Analytic Function in the Unit Disk

LinkBack

Thread Tools

Display

Analytic Function in the Unit Disk

Re: Analytic Function in the Unit Disk

Similar Math Help Forum Discussions

[SOLVED] Area of a holomorphic function's range on the unit disk

fixed points of sin in the complex unit disk

Connected Unit Disk

conformal map, unit disk

Mobius-induced inequality on the unit disk.

Search Tags