Sharing values and normality. (English) Zbl 0758.30028

Schwick, Wilhelm

Arch. Math. 59, No. 1, 50-54 (1992).

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.

Reviewer: W.Schwick (Dortmund)

MSC:

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

Keywords:

normal family; value sharing; Nevanlinna theory; meromorphic function

Citations:

Zbl 0416.30028

References:

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