Open Access
september 2012 Normal families of holomorphic functions and multiple values
Lijuan Zhao, Xiangzhong Wu
Bull. Belg. Math. Soc. Simon Stevin 19(3): 535-547 (september 2012). DOI: 10.36045/bbms/1347642381

Abstract

Let $\mathcal{F}$ be a family of holomorphic functions defined in $D \subset C$, and let $ k, m, n, p $ be four positive integers with $ \frac{k+p+1}{m}+\frac{p+1}{n} < 1 $. Let $\psi (\not \equiv 0, \infty )$ be a meromorphic function in $ D $ and which has zeros only of multiplicities at most $ p $. Suppose that, for every function $ f \in \mathcal{F} $, (i) $ f $ has zeros only of multiplicities at least $ m $; (ii) all zeros of $ f^{(k)}-\psi(z) $ have multiplicities at least $ n $; (iii) all poles of $ \psi $ have multiplicities at most $ k $, and (iv) $ \psi(z) $ and $ f(z) $ have no common zeros, then $\mathcal{F}$ is normal in $ D $.

Citation

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Lijuan Zhao. Xiangzhong Wu. "Normal families of holomorphic functions and multiple values." Bull. Belg. Math. Soc. Simon Stevin 19 (3) 535 - 547, september 2012. https://doi.org/10.36045/bbms/1347642381

Information

Published: september 2012
First available in Project Euclid: 14 September 2012

MathSciNet: MR3027359
zbMATH: 1267.30088
Digital Object Identifier: 10.36045/bbms/1347642381

Subjects:
Primary: 30D35 , 30D45

Keywords: Holomorphic functions , multiplicity , normal family

Rights: Copyright © 2012 The Belgian Mathematical Society

Vol.19 • No. 3 • september 2012
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