| 刘丹,杨德贵,方明亮.涉及分担值的正规定则[J].数学年刊A辑,2017,38(3):277~288 |
| 涉及分担值的正规定则 |
| Some Normal Criteria Concerning Shared Values |
| Received:June 05, 2015 Revised:August 24, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0023 |
| 中文关键词: Meromorphic function, Normality, Shared value |
| 英文关键词:Meromorphic function, Normality, Shared value |
| 基金项目:本文受到国家自然科学基金(No.11371149;No.61375006)和华南农业大学数学与信息学院院长基金\的资助. |
| Author Name | Affiliation | E-mail | | LIU Dan | Department of Mathematics, College of Mathematics and Informatics, South China Agricultural University,Guangzhou 510642, China. | liudan@scau.edu.cn | | YANG Degui | Department of Mathematics, College of Mathematics and Informatics, South China Agricultural University,Guangzhou 510642, China. | dyang@scau.edu.cn | | FANG Mingliang | Department of Mathematics, College of Mathematics and Informatics, South China Agricultural University,Guangzhou 510642, China. | mlfang@scau.edu.cn |
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| 中文摘要: |
| 设 $\mathcal F$是区域 $D$上的一个亚纯函数族,
$k\ (\geq 2)$是一个正整数, $b$是一个非零复数, $M$是一个正数.
若对任意给定的 $f \in \mathcal F$, $f$的零点重数至少为$k$, 且$f(z)=0 \Rightarrow |f^{(k)}(z)| \leq M$.
如果对任意给定的函数 $f,g \in \mathcal F$, $L(f)$与 $L(g)$的零点都为重零点,
且$L(f)$与$L(g)$在区域 $D$内分担$b$, 则$\mathcal F$在区域 $D$内正规. |
| 英文摘要: |
| Let $\mathcal F$ be a family of meromorphic
functions in a domain $D$, $k\ (\geq 2)$ a positive integer, $b$
a nonzero finite complex number, and $M$ a positive number.
Suppose that for each $f \in \mathcal F$, all zeros of $f$
have multiplicity at least $k$, and $f(z)=0 \Rightarrow |f^{(k)}(z)| \leq M$.
If for each pair $f,g \in \mathcal F$, all zeros of $L(f)$ and $L(g)$ are multiple,
and $L(f)$ and $L(g)$ share $b$ in $D$, then $\mathcal F$ is normal in $D$. |
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