Find all analytics functions in the domain $\Omega=\{z\in\mathbb{C}; |z|< R\}$ that satisfy $f(0)=e^{i}$ and $|f(z)|\leq 1$ for each $z\in\Omega$.
I try to write a series,i.e., $f(z)=\sum_{n=0}^{\infty}{a_{n}z^{n}}$, then $f(0)=a_{0}=e^{i}$, but I do not get any result. Any help please !