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Some normality criteria of function families concerning shared values. (English) Zbl 1273.30023
Summary: We study the normality of families of meromorphic functions related to shared values. We mainly consider whether a family of meromorphic functions \(\mathcal F\) is normal in a domain \(D\), if (i) for every pair of functions \(f\) and \(g\) in \(\mathcal F\), \(f^{(k)} - af^{n}\) and \(g^{(k)} - ag^{n}\) share the value \(b\), and (ii) \(f\) has no zero of multiplicity less than \(k\) in \(D\) for every function \(f \in \mathcal F\), where \(a\) and \(b\) are two finite complex numbers such that \(a \neq 0\), \(n\geq k+3\) and \(k \geq 2\) are two positive integers. An example shows that the condition (ii) in our results is best possible.

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