Representation With Majorant of the Schwarz Lemma at the Boundary


Bülent Nafi Örnek, Tuğba Akyel




Let $f$ be a holomorphic function in the unit disc $D$ and $|f(z)-1|<1$ for $|z|<1$. We generalize a uniqueness portion of Schwarz's lemma and provide sufficient conditions on the local behavior of $f$ near a finite set of boundary points that needs $f$ to be a finite Blaschke product.