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Exceptional functions and normality. (English) Zbl 0883.30023

L. Yang [Indiana Univ. Math. J. 35, 179-191 (1986; Zbl 0589.30027)] proved that a family \({\mathcal F}\) of functions \(f(z)\) meromorphic in a domain \(G\) is normal if \(f(z)- z\) and \(f^{(k)}(z)- z\), \(k\) a fixed integer \(\geq 1\), have no zeros in \(G\) for every \(f \in {\mathcal F}\). The author generalizes this result to the case that \(f(z)- \psi_{1}(z)\) and \(f^{(k)}(z)- \psi_{2}(z)\) have no zeros in \(G\) for every \(f \in {\mathcal F}\), where \(\psi_{1}\) and \(\psi_{2}\) are analytic in \(G\) and \(\psi_{1}^{(k)} \not\equiv \psi_{2}\).

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

Citations:

Zbl 0589.30027
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