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A note on normality and shared values

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Mingliang Fang  and
Lawrence Zalcman
Mingliang Fang
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097 P. R., China, e-mail: mlfang@pine.njun.edu.cn
Lawrence Zalcman
Affiliation:
Department of Mathematics and Statistics, Bar-Ilan University52900 Ramat-Gan, Israel e-mail: zalcman@macs.biu.ac.il
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Abstract

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Let k be a positive integer and b a nonzero constant. Suppose that F is a family of meromorphic functions in a domain D. If each function f ∈ F has only zeros of multiplicity at least k + 2 and for any two functions f, g ∈ F, f and g share 0 in D and f(k) and g(k) share b in D, then F is normal in D. The case f ≠ 0, f(k) ≠ b is a celebrated result of Gu.

Keywords

meromorphic functionnormalityshared value

MSC classification

Secondary: 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 141 - 150
Copyright
Copyright © Australian Mathematical Society 2004

References

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