Bull. Korean Math. Soc. 2016; 53(5): 1373-1384
Online first article September 12, 2016 Printed September 30, 2016
https://doi.org/10.4134/BKMS.b150673
Copyright © The Korean Mathematical Society.
Qiaoyu Chen and Jianming Qi
Shanghai Lixin University of Accounting and Finance, Shanghai Dianji University
In this paper, we research the normality of sequences of meromorphic functions concerning the sequence of omitted functions. The main result is listed below. Let $\{f_{n}(z)\}$ be a sequence of functions meromorphic in $D$, the multiplicities of whose poles and zeros are no less than $k+2,~k\in \mathbb N$. Let $\{b_{n}(z)\}$ be a sequence of functions meromorphic in $D$, the multiplicities of whose poles are no less than $ k+1$, such that $b_{n}(z)\overset\chi\Rightarrow b(z)$, where $b(z)(\neq 0)$ is meromorphic in $D$. If $f^{(k)}_{n}(z)\ne b_{n}(z)$, then $\{f_{n}(z)\}$ is normal in $D$. And we give some examples to indicate that there are essential differences between the normal family concerning the sequence of omitted functions and the normal family concerning the omitted function. Moreover, the conditions in our paper are best possible.
Keywords: meromorphic functions, normal family, sequence of omitted functions
MSC numbers: Primary 30D45; Secondary 30D35
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