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Normality criteria concerning sharing values - MaRDI portal

Normality criteria concerning sharing values (Q1283643)

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scientific article; zbMATH DE number 1275972
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Normality criteria concerning sharing values
scientific article; zbMATH DE number 1275972

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    Normality criteria concerning sharing values (English)
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    8 October 1999
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    Meromorphic functions \(f\) and \(g\) share a complex value \(c\) if \(f^{-1}(\{c\})=g^{-1}(\{c\})\) (ignore the multiplicity). The author proves the following. Theorem: Let \({\mathfrak F}\) be a family of holomorphic functions in a domain \(G\) and let \(b\neq 0\). If for every \(f\in{\mathfrak F}\) the functions \(f\) and \(f'\) share 0 and \(b\), then \({\mathfrak F}\) is a normal family.
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    holomorphic functions
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    sharing values
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    normal families
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