On the growth of nonvanishing analytic functions

Abstract

In this article by a new and simple method we derive new and old coefficient bounds and distortion theorems for functions G(z) analytic in the unit disk and satisfying sup(|G(z)|(1 - |z|2)a) ≦ 1 for some a ≧ 0. These results enable us to |z|<1 prove analogous theorems for the subclasses consisting of nonvanishing functions.