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Normal families of holomorphic functions

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Huai-Hui Chen  and
Xin-Hou Hua
Huai-Hui Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210024, P.R., China
Xin-Hou Hua
Affiliation:
Department and Institute of Mathematics, Nanjing University, Nanjing 210008, P.R., China.
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Abstract

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Let a(z) be a meromorphic function with only simple poles, and let k∈ N. Suppose that f(z) is meromorphic. We first set up an inequality in which T(r, f) is bounded by the counting function of the zeros of f(k) + af2, and then we prove a corresponding normal criterion. An example shows that the restriction on the poles of a(z) is best possible.

MSC classification

Secondary: 30D45: Bloch functions, normal functions, normal families 30D35: Distribution of values, Nevanlinna theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 112 - 117
Copyright
Copyright © Australian Mathematical Society 1995

References

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