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Shared sets and normal families of meromorphic functions. (English) Zbl 1207.30042

The main result of this paper is:
Let \(F\) be a family of meromorphic functions in a domain \(D\), let \(a_1, a_2\), and \(a_3\) be three distinct finite nonzero complex numbers, and let \(S=\{a_1,a_2,a_3\}\). If for every \(f\in F\),
\[ f(z)\in S\Longrightarrow f'(z)\in S, \] then \(F\) is normal in \(D\).

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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References:

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