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Sharing values and normality. (English) Zbl 0758.30028

E. Mues and N. Steinmetz [Manusc. Math. 29, 195-206 (1979; Zbl 0416.30028)] proved that a nonconstant meromorphic function \(f\) in the plane, which shares three complex values with its first derivative, satisfies \(f\equiv f'\). We prove that a family \(F\) of meromorphic functions in a domain \(G\), where every \(f\in F\) shares three fixed complex values with \(f'\), is normal.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D45 Normal functions of one complex variable, normal families

Citations:

Zbl 0416.30028
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References:

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