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Zbl 1051.30020
Xu, Neng; Yang, Dinggong
On starlikeness and close-to-convexity of certain meromorphic functions.
(English)
[J] J. Korea Soc. Math. Educ., Ser. B, Pure Appl. Math. 10, No. 1, 1-11 (2003). ISSN 1226-0657

Let $\Sigma_n$ $(n= 1,2,\dots)$ denote the class of functions of the form $$f(z)= {1\over z}+ \sum^\infty_{m=n-1} a_mz^m,$$ which are analytic in the punctured unit disc $E_0= \{z: 0<\vert z\vert< 1\}$. Let $\Sigma^*_n(\alpha)\subset\Sigma_n$ be the subclass of meromorphic starlike functions of order $\alpha$ $(0\le\alpha< 1)$. In this paper the authors obtain sufficient conditions on $f\in\Sigma_n$ so that $f$ belongs to $\Sigma^*_n(\alpha)$ for a suitable $\alpha$. The conditions involve subordination properties of expressions associated to $f$ which are too complicated to be reproduced here.
MSC 2000:
*30C45 Special classes of univalent and multivalent functions

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