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NORMALITY AND SHARED SETS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  01 June 2009

MINGLIANG FANG  and
LAWRENCE ZALCMAN
MINGLIANG FANG
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, PR China (email: hnmlfang@hotmail.com)
LAWRENCE ZALCMAN*
Affiliation:
Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel (email: zalcman@macs.biu.ac.il)
*
✉For correspondence; e-mail: zalcman@macs.biu.ac.il
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Abstract

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Let ℱ be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k+1. Let a and b be distinct finite complex numbers, and let k be a positive integer. If, for each pair of functions f and g in ℱ, f(k) and g(k) share the set S={a,b}, then ℱ is normal in D. The condition that the zeros of functions in ℱ have multiplicity at least k+1 cannot be weakened.

Keywords

meromorphic functionnormalityshared set

MSC classification

Secondary: 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 339 - 354
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The research of the first author was supported by the NNSF of China (Grant No. 10771076) and the NSF of Guangdong Province, China. The research of the second author was supported by the German–Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003.

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