Radius estimates of a subclass of univalent functions

Abstract

For analytic functions $f$ normalized by$f(0)=f^{\prime }(0)-1=0$ in the open unit disk $U$, a class$P_{\alpha }(\lambda )$ of $f$ defined by$|D_z^{\alpha }(\frac{z}{f(z)})|\le \lambda$, where$D_z^{\alpha }$ denotes the fractional derivative of order $\alpha$, $m\le \alpha <m+1$, $mın{N}_0$, is introduced. Inthis article, we study the problem when $\frac{1}{r}f(rz)ın{P}_{\alpha }(\lambda )$, $3\le \alpha <4$.