Hayman's alternative and normal families of non-vanishing meromorphic functions
type: Item
instance of: scholarly article
title: Hayman's alternative and normal families of non-vanishing meromorphic functions
zbMATH Open document ID: 1062.30033
DOI: 10.1007/BF03321861
author: Jürgen Grahl
published in: Computational Methods and Function Theory
publication date: 2004-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 30D45
zbMATH DE Number: 2103480
zbMATH Keywords: Hayman's alternative
zbMATH Keywords: normal family
zbMATH Keywords: non-vanishing
zbMATH Keywords: meromorphic function
reviewed by: Martin Chuaqui
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03321861
OpenAlex ID: W2079999164
description: scientific article; zbMATH DE number 2103480