Koebe Domain of Starlike Functions of Complex Order with Montel Normalization

Abstract

Let $S^{\ast }(1-b)$ ($b\ne 0$ complex) denote the class of functions $f(z)=z+{\alpha }_2{z}^2+...$ analytic in $D=z\mid |z|<1$ which satisfies,for $z=e^{i\theta }\in D$, $(f(z)/z)\ne 0$ in D, and $Re[1+\frac{1}{b}(z\frac{f^{{}^{\prime }}(z)}{f(z)}-1\left)\right]>0$. The aim of this paper is to give the Koebe domain of the above mentioned class.

4 pages, TeX