On close-to-star functions

Abstract

For a given class $A$ and a set $D$ the sets $\bigcap_{f\in A}f(D)$ and $\bigcup_{f\in A}f(D)$ are called the Koebe set and the covering set for $A$ over $D$, respectively. These sets are found for the class $H$ of close-to-star functions $f$ of the form $f(z)=\frac{z}{1-z^2}p(z)$, where $Re p(z)>0, p(0)=1$. Analogous results concerning some other subclasses of close-to-star functions are established too.