Univalence of quotient of analytic functions

摘要

Let A denote the family of all analytic functions f in the unit disk D with the normalization f(0)=0=f′(0)-1. In this note, we mainly consider the radius of univalence of F defined by F(z)=z2/f(z), where f belongs to some subclasses of A or S, the class of univalent functions from A. The results of the present article sharpen the earlier known results.