Koebe Domain of Starlike Functions of Complex Order with Montel Normalization

Abstract

Let $S^{*}(1-b)$ ($b \not= 0$ complex) denote the class of functions $f(z)=z+\alpha_{2}z^{2}+...$ analytic in $D={z \mid | z | < 1}$ which satisfies,for $z=e^{i\theta} \in D$, $(f(z)/z)\not= 0$ in D, and $Re \Biggr [ 1+ {1 \over b} \Biggr (z {{f^{'}(z)} \over f(z)}-1 \Biggl) \Biggl ] > 0$. The aim of this paper is to give the Koebe domain of the above mentioned class.