Hayman’s Alternative and Normal Families of Non-vanishing Meromorphic Functions
Copyright policy )Hayman’s Alternative and Normal Families of Non-vanishing Meromorphic Functions
Let \(P\) be a differential polynomial satisfying certain technical and general conditions. The author shows that a family \(\mathcal{F}\) of non-vanishing meromorphic functions in the unit disk \(\mathbb{D}\) such that \(P[f](z)\neq 1\) for all \(z\in\mathbb{D}\) and all \(f\in\mathcal{F}\), is normal. This generalizes former results of \textit{W. Schwick} [Complex Variables, Theory Appl. 32, 51--57 (1997; Zbl 0938.30021)] and of \textit{M.-L. Fang} [Acta Math. Sin. 37, 86--90 (1994; Zbl 0796.30030)]. Furthermore, the author gives corresponding Picard type theorems generalizing Hayman's alternative.
- University of Würzburg Germany
non-vanishing, meromorphic function, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Normal functions of one complex variable, normal families, Hayman's alternative, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, normal family
non-vanishing, meromorphic function, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Normal functions of one complex variable, normal families, Hayman's alternative, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, normal family
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