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December 1993 New criteria for meromorphic $p$-valent starlike functions
M.K. Aouf, H.M. Hossen
Tsukuba J. Math. 17(2): 481-486 (December 1993). DOI: 10.21099/tkbjm/1496162274

Abstract

Let $B_{n}(\alpha)$ be the class of functions of the form $f(z)=\frac{a_{-p}}{z^{p}}+\sum_{k=0}^{\infty}$ $(a_{-p}\neq 0, p\in N=\{1,2, \cdots\})$ which are regular in the punctured disc$U^{*}=\{z:0 \lt |z| \lt 1\}$ and satisfying ${\rm Re}\{\frac{D^{n+1}f(z)}{D^{n}f(z)}-(p+1)\} \lt -\alpha$ $(n\in N_{0}=\{0,1, \cdots\}, |z| \lt 1,0\leqq\alpha \lt p)$, where $D^{n}f(z)=\frac{a_{-p}}{z^{p}}+\sum_{m=1}^{\infty}(p+m)^{n}a_{m-1}z^{m-1}$ It is proved that $B_{n+1}(\alpha)\subset B_{n}(\alpha)$. Since $B_{0}(\alpha)$ is the class of meromorphically $p$-valent starlike functions of order $\alpha$, all functions in $B_{n}(\alpha)$ are $p$-valent starlike. Further a property preserving integrals is considered.

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M.K. Aouf. H.M. Hossen. "New criteria for meromorphic $p$-valent starlike functions." Tsukuba J. Math. 17 (2) 481 - 486, December 1993. https://doi.org/10.21099/tkbjm/1496162274

Information

Published: December 1993
First available in Project Euclid: 30 May 2017

zbMATH: 0804.30012
MathSciNet: MR1255485
Digital Object Identifier: 10.21099/tkbjm/1496162274

Rights: Copyright © 1993 University of Tsukuba, Institute of Mathematics

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Vol.17 • No. 2 • December 1993
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