Show that there is no holomorphic fuction $f$ in the unit disc $D$ that extends continuously to boundary of $D$ such that $f(z)=\frac{1}{z} ~for~ z\in \partial( D) $.
I tried to apply maximum principle but I couln't find the way to prove it.
Help me please.
I just update the full statement and I think it probably assume it is not constant fuction.
Thank you.