Let $f(z)=a_pz^p -\sum_{n=1}^{\infty} a_{n+k}z^{n+k}$, $k\ge p\ge 1$, with $a_p>0$, $a_{n+k}\ge0$ be regular in $U=\{z:|z|<1\}$ and $F(z)=(1-\lambda)f(z)+\lambda p^{-1}zf'(z)$, $z\in U$, where $\lambda\ge 0$.