Revista Matemática Iberoamericana

Quasinormal Families of Meromorphic Functions

Shahar Nevo, Xuecheng Pang, and Lawrence Zalcman

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Abstract

Let $\mathcal{F}$ be a family of functions meromorphic on the plane domain $D$, all of whose zeros are multiple. Suppose that $f'(z)\ne 1$ for all $f\in \mathcal{F}$ and $z\in D.$ Then if $\mathcal{F}$ is quasinormal on $D$, it is quasinormal of order 1 there.

Article information

Source
Rev. Mat. Iberoamericana, Volume 21, Number 1 (2005), 249-262.

Dates
First available in Project Euclid: 22 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1114176234

Mathematical Reviews number (MathSciNet)
MR2155021

Zentralblatt MATH identifier
1084.30037

Subjects
Primary: 30D45: Bloch functions, normal functions, normal families

Keywords
quasinormal families omitted values

Citation

Pang, Xuecheng; Nevo, Shahar; Zalcman, Lawrence. Quasinormal Families of Meromorphic Functions. Rev. Mat. Iberoamericana 21 (2005), no. 1, 249--262. https://projecteuclid.org/euclid.rmi/1114176234


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References

  • Bergweiler, W. and Langley, J.K.: Multiplicities in Hayman's alternative. J. Aust. Math. Soc. 78 (2005), 37-57.
  • Chuang, C.-T.: Normal Families of Meromorphic Functions. World Scientific Publishing. River Edge, NJ, 1993.
  • Ku, Y.X.: Un critère de normalité des familles de fonctions méromorphes. Sci. Sinica Special Issue 1 (1979), 267-274 (Chinese).
  • Nevo, S.: On theorems of Yang and Schwick. Complex Variables Theory Appl. 46 (2001), 315-321.
  • Nevo, S.: Applications of Zalcman's lemma to $Q_m$-normal families. Analysis 21 (2001), 289-325.
  • Pang, X.C. and Zalcman, L.: Normal families and shared values. Bull. London Math. Soc. 32 (2000), 325-331.
  • Pang, X.C. and Zalcman, L.: Normal families of meromorphic functions with multiple zeros and poles. Israel J. Math. 136 (2003), 1-9.
  • Wang, Y.F. and Fang, M.L.: Picard values and normal families of meromorphic functions with multiple zeros. Acta Math. Sinica (N.S.) 14 (1998), 17-26.
  • Zalcman, L.: Normal families: new perspectives. Bull. Amer. Math. Soc. (N.S.) 35 (1998), 215-230.