Acta Mathematica Sinica, English Series

, Volume 35, Issue 12, pp 1972–1978 | Cite as

A Normal Criterion Concerning Omitted Holomorphic Function

  • Jin Hua YangEmail author
  • Qi YangEmail author
  • Xue Cheng PangEmail author


In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let \(\mathcal{F}\) be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) ≢ 0 and f(z) ≢ ∞ whenever a(z) = 0. If for any \(f \in \mathcal{F}\), f′(z) − a(z)fk(z) ≠ b(z), then \(\mathcal{F}\) is normal on D.


Normal family holomorphic functions omitted functions 

MR(2010) Subject Classification

30D35 30D45 


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We would like to thank Professor Mingliang Fang for raising the questions made to this paper.


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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesXinjiang Normal UniversityUrumqiP. R. China
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiP. R. China

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