@article {
author = {Rahrovi, Samira},
title = {Parabolic starlike mappings of the unit ball $B^n$},
journal = {Sahand Communications in Mathematical Analysis},
volume = {03},
number = {1},
pages = {63-70},
year = {2016},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {},
abstract = {Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^n\subseteq\mathbb{C}^n$ given by $$\Phi_{n,\gamma}(f)(z)=\left(f(z_1),(f'(z_1))^\gamma\hat{z}\right),$$ where $\gamma\in[0,1/2]$, $z=(z_1,\hat{z})\in B^n$ and $$\Psi_{n,\beta}(f)(z)=\left(f(z_1),(\frac{f(z_1)}{z_1})^\beta\hat{z}\right),$$ in which $\beta\in[0,1]$, $f(z_1)\neq 0$ and $z=(z_1,\hat{z})\in B^n$. 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 $B^n$.},
keywords = {Roper-Suffridge extention operator,Biholomorphic mapping,Parabolic starlike function},
url = {https://scma.maragheh.ac.ir/article_17820.html},
eprint = {https://scma.maragheh.ac.ir/article_17820_b9493019b43e586b7325e86fcd33c0a4.pdf}
}