Radius estimates of a subclass of univalent functions

Abstract

For analytic functions $f$ normalized by$f(0)=f'(0)-1=0$ in the open unit disk $U$, a class$P_{\alpha}(\lambda)$ of $f$ defined by$|D^{\alpha}_{z}(\frac{z}{f(z)})|\leq \lambda$, where$D^{\alpha}_{z}$ denotes the fractional derivative of order $\a$, $m\leq \alpha < m+1$, $m ın N_{0} $, is introduced. Inthis article, we study the problem when $\frac{1}{r} f(rz) ınP_{\alpha}(\lambda)$, $3 \leq \alpha < 4$.