Univalency of certain transform of univalent functions

Abstract

We consider univalency problem in the unit disc $\mathbb{D}$ of the function $$g(z)=\frac{(z/f(z))-1}{-a_2},$$ where $f$ belongs to some classes of univalent functions in $\mathbb{D}$ and $a_2=\frac{f^{\prime \prime }(0)}{2}\ne 0$.