A criterion of normality concerning holomorphic functions whose derivative omit a function II

Abstract

The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D ⊂ ℂ, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h(z) ≢ 0 and ∞ be a meromorphic function on D. Assume that the following two conditions hold for every f ∈ F: $\begin{gathered} (a)f(z) = 0 \Rightarrow |f^{(k)} (z)| < |h(z)|. \hfill \\ (b)f^{(k)} (z) \ne h(z). \hfill \\ \end{gathered} $ Then F is normal on D.

Keywords

Normal family / Meromorphic functions / Omitted function

References

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