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.


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


Zbl 0416.30028
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