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A normal criterion about two families of meromorphic functions concerning shared values. (English) Zbl 1267.30086

Summary: In this paper, we mainly discuss the normality of two families of functions concerning shared values and prove the following:
Let \( \mathcal F \) and \(\mathcal G \) be two families of functions meromorphic on a domain \( D \subset \mathbb C\) and let \(a_1, a_2, a_3, a_4\) be four distinct finite complex numbers. If \(\mathcal G \) is normal and for every \( f \in \mathcal F \) there exists \( g \in \mathcal G \) such that \( f (z)\) and \( g (z)\) share the values \( a_1\), \( a_2\), \( a_3\), \( a_4\), then \(\mathcal F \) is normal in \( D \).

MSC:

30D45 Normal functions of one complex variable, normal families
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References:

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