parabolic starlike mappings of the unit ball $b^n$

let $f$ be a locally univalent function on the unit disk $u$. we consider the normalized extensions of $f$ to the euclidean unit ball $b^nsubseteqmathbb{c}^n$ given by$$phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in b^n$ and$$psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$in which $betain[0,1]$, $f(z_1)neq 0$ and $z=(z_1,hat{z})inb^n$. in the case $gamma=1/2$, the function $phi_{n,gamma}(f)$ reduces to the well known roper-suffridge extension operator. by using different methods, we prove that if $f$ is parabolic starlike mapping on $u$ then $phi_{n,gamma}(f)$ and $psi_{n,beta}(f)$ are parabolic starlike mappings on $b^n$.