Parabolic starlike mappings of the unit ball $B^n$

نویسنده

  • Samira Rahrovi Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.
چکیده مقاله:

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 $z=(z_1,hat{z})in B^n$. 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 $B^n$.

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

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عنوان ژورنال

دوره 03  شماره 1

صفحات  63- 70

تاریخ انتشار 2016-02-01

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