Arkiv för Matematik

  • Ark. Mat.
  • Volume 43, Number 2 (2005), 307-321.

Normality and fixed-points of meromorphic functions

Jianming Chang, Mingliang Fang, and Lawrence Zalcman

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Abstract

LetF be families of meromorphic functions in a domain D, and let R be a rational function whose degree is at least 3. If, for any f∈F, the composite function R(f) has no fixed-point in D, thenF is normal in D. The number 3 is best possible. A new and much simplified proof of a result of Pang and Zalcman concerning normality and, shared values is also given.

Article information

Source
Ark. Mat., Volume 43, Number 2 (2005), 307-321.

Dates
Received: 8 January 1994
Revised: 30 May 1994
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898902

Digital Object Identifier
doi:10.1007/BF02384782

Mathematical Reviews number (MathSciNet)
MR2173954

Zentralblatt MATH identifier
1095.30026

Rights
2005 © Institut Mittag-Leffler

Citation

Chang, Jianming; Fang, Mingliang; Zalcman, Lawrence. Normality and fixed-points of meromorphic functions. Ark. Mat. 43 (2005), no. 2, 307--321. doi:10.1007/BF02384782. https://projecteuclid.org/euclid.afm/1485898902


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