May you help me with this question:
Let $F$ a familiy of analytic functions at $H=\{z:\mathrm{Im}z>0\}$ that satisfies $f(i)=0$ and $|f(z)|\leq 1$.
I want to find $\sup\limits_{f \in F}|f(2i)|$.
I think that the solution is based on Möbius transformation.
Thank you.