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NORMAL FAMILIES OF ZERO-FREE MEROMORPHIC FUNCTIONS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  16 November 2011

BINGMAO DENG ,
MINGLIANG FANG  and
DAN LIU
BINGMAO DENG
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: dbmao2012@163.com)
MINGLIANG FANG*
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: mlfang@scau.edu.cn)
DAN LIU
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: liudan@scau.edu.cn)
*
✉For correspondence; e-mail: mlfang@scau.edu.cn
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Abstract

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Let ℱ be a family of zero-free meromorphic functions in a domain D, let h be a holomorphic function in D, and let k be a positive integer. If the function f(k)−h has at most k distinct zeros (ignoring multiplicity) in D for each f∈ℱ, then ℱ is normal in D.

Keywords

meromorphic functionnormalityzero-free

MSC classification

Secondary: 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 313 - 322
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Research supported by the NNSF of China (Grant No. 11071083).

References

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