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Some simple criteria of starlikeness for meromorphic functions. (English) Zbl 1224.30040

Authors’ abstract: “We use the theory of differential subordinations to obtain a new condition for meromorphic functions, defined in the punctured unit disc \(\{z\in\mathbb C\setminus\{ 0\} : | z| <1\}\), which are of the form \(f(z)=\frac1z+a_nz^n+a_{n+1}z^{n+1}+\cdots\), to be starlike functions. The new condition for starlikeness is expressed by means of \(| (1-\alpha)zf(z)+z^2f'(z)+\alpha| \), where \(\alpha\in[0,1)\).”

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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