Certain bounded functions of complex order

M. K. Aouf, A. O. Mostafa

In this paper we obtain sharp coefficient bounds for functions analytic in the unit disc $U$ and belonging to the class $R(b,M)$, $b\neq 0$ is a complex number. Also, we maximize $| a_{3}-\mu a_{2}^{2}| $ over the class $R(b,M)$ and obtain distortion theorem for functions in this class.