Rouché type theorems and a theorem of Adamyan, Arov and Krein

Abstract

We show Rouché type theorems using a theorem of Adamyan, Arov and Krein. As applications, we obtain a certain characterization of self-maps of the unit disc in terms of the location of the Denjoy-Wolf point and we study a function in the Smirnov class whose real part is positive.