Normal families concerning shared values
type: Item
instance of: scholarly article
title: Normal families concerning shared values
zbMATH Open document ID: 0960.30027
DOI: 10.1007/BF02810596
author: Xinhou Hua
author: Huaihui Chen
published in: Israel Journal of Mathematics
publication date: 2000-04-26T00:00:00Z
review text: Let \(F\) be a family of analytic functions in the unit disk \(D\). Suppose there is a nonzero complex number \(a\) such that for each \(f\) in \(F\), \(f\), \(f'\), and \(f''\) all share the value \(a\) ignoring multiplicity. Using Zalcman's principle the authors show \(F\) is a normal family. Since the family \(G= \{f_n|f_n(z)= \exp(nz)\) for \(n=1,2,\dots\}\) is not normal, the value \(a\) cannot be zero. Related results appear in \textit{W. Schwick} [Arch. Math. 59, No. 1, 50-54 (1992; Zbl 0758.30028)] and \textit{G. Jank}, \textit{E. Mues} and \textit{L. Volkmann} [Complex Variables, Theory Appl. 6, 51-71 (1986; Zbl 0603.30037)].
Mathematics Subject Classification ID: 30D45
zbMATH DE Number: 1436114
zbMATH Keywords: normal family
reviewed by: Linda R. Sons
MaRDI profile type: Publication
cites work: Q4752726
cites work: Q5723337
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cites work: Meromorphe funktionen, die mit ihrer ersten und zweiten ableitung einen endlichen wert teilen
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description: scientific article; zbMATH DE number 1436114