Starlikeness of sections of univalent functions

Let ${\S}$ be the class of all normalized analytic and univalent functions in the unit disk $\ID$. In this paper, we determine condition so that each section $s_{n}(f,z)$ of $f\in {\S}$ is starlike in the disk $|z|\lt r_n$. In particular, $s_{n}(f,z)$ is starlike in $|z|\leq 1/2$ for $n \geq 47$.