On a subclass of Bazileviv c functions

Abstract

For $\alpha>0$, $0\le \beta<1$, we denote $B_1(\alpha,\beta)$ to be the class of normalised analytic functions satisfying the condition $Re\Big({f(z)\over z}\Big)^{\alpha-1}f'(z)>\beta$ for $z$ in the unit disc $D=\{z:|z|<1\}$. Sharp estimates for $Re\Big({f(z)\over z}\Big)^\alpha$ is established. In fact a more generalished result concerning iterated integrals is obtained.