Abstract

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.

Keywords: Analytic functions; complex order; starlike functions; bounded functions.

MSC: 30C45

Pages:  109$-$116     

Volume  62 ,  Issue  2 ,  2010