Archiv der Mathematik

, Volume 88, Issue 6, pp 560–568 | Cite as

Normal families and multiple values



Let \({{\mathcal{F}}}\) be a family of meromorphic functions in a domain D, and let k be a positive integer, and let b be a nonzero complex number. If, for each \(f \in {{\mathcal{F}}}\), f ≠ 0, \(f^{(k)} \neq 0\) and the zeros of \(f^{(k)} - b\) have multiplicity at least 3 for k = 1 and 2 for k ≥ 2, then \({{\mathcal{F}}}\) is normal in D. Examples show that the multiplicity of the zeros of \(f^{(k)} - b\) is best possible.

Mathematics Subject Classification (2000).



Meromorphic function normal families multiplicity 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Institute of Applied MathematicsSouth China Agricultural UniversityGuangzhouP. R. China
  2. 2.Department of MathematicsChangshu Institute of TechnologyJiangsuP. R. China

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