CONVOLUTIONS OF UNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS

Abstract

Let $f(z)=z+\sum_{n=2}^\infty a_n z^n$, $a_n\ge 0$ and $g(z)=z+\sum_{n=2}^\infty b_n z^n$, $b_n\ge 0$. We investigate some properties of $h(z) = f(z) *g(z) =z+\sum_{n=2}^\infty a_nb_n z^n$ where $f(z)$ and $g(z)$ belong to certain subclasses of starlike and convex functions.