Computational Methods and Function Theory

, Volume 2, Issue 1, pp 257–265 | Cite as

Normal Families of Meromorphic Functions whose Derivatives Omit a Function

  • Xuecheng Pang
  • Degui Yang
  • Lawrence Zalcman


Let \(\cal F\) be a family of functions meromorphic on the plane domain D, and let h be a holomorphic function on D, h n= 0. Suppose that, for each \(f \in {\cal F}\), f (m)(z) ≠ h(z) for zD. Then \(t\cal F\) is normal on D (i) if all zeros of functions in \(\cal F\) have multiplicity at least m + 3, or (ii) if all zeros of functions in \(\cal F\) have multiplicity at least m + 2 and h has only multiple zeros on D, or (iii) if all poles of functions in \(\cal F\) are multiple and all zeros have multiplicity at least m + 2.


Normal families omitted functions 

2000 MSC



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Copyright information

© Heldermann  Verlag 2002

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiP. R. China
  2. 2.College of SciencesSouth China Agricultural UniversityGuangzhouP. R. China
  3. 3.Department of Mathematics and StatisticsBar-Ilan UniversityRamat-GanIsrael

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