Radius estimates of a subclass of univalent functions

Maslina Darus, Rabha W. Ibrahim

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 $\a$, $m eq lpha < m+1$, $m n N_{0} $, is introduced. In this article, we study the problem when $\frac{1}{r} f(rz) \in P_{lpha}(ambda)$, $3 eq lpha < 4$.