Normality and shared values concerning differential polynomials
type: Item
instance of: scholarly article
title: Normality and shared values concerning differential polynomials
zbMATH Open document ID: 1213.30055
published in: Science China. Mathematics
publication date: 2010-05-26T00:00:00Z
review text: Let \({\mathcal F}\) be a family of meromorphic functions in a domain \(D\), and let \(P\) be a polynomial with either \(\deg P \geq 3\) or \(\deg P=2\), and \(P\) having only one zero. In this paper, the authors prove that if there is a non-zero complex number \(b\) such that, for any \(f \in {\mathcal F}\) and \(g \in {\mathcal F}\), \(P(f)f'\) and \(P(g)g'\) share \(b\) in \(D\), then \({\mathcal F}\) is normal in \(D\). The authors also give two examples showing that the theorem fails when \(\deg P=1\) or \(b=0\).
reviewed by: Zhuan Ye
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D45
zbMATH DE Number: 5712120
zbMATH Keywords: meromorphic function
zbMATH Keywords: normal family
zbMATH Keywords: shared value
author: Chunlin Lei
author: Mingliang Fang
MaRDI profile type: Publication
full work available at URL: s11425-010-0059-x
OpenAlex ID: W2368639645
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DOI: 10.1007/S11425-010-0059-X
description: scientific article; zbMATH DE number 5712120