| 邓炳茂,刘 丹,杨德贵.涉及分担函数的正规定则[J].数学年刊A辑,2016,37(3):261~266 |
| 涉及分担函数的正规定则 |
| Normality Concerning Shared Functions |
| Received:April 12, 2015 Revised:September 20, 2015 |
| DOI： |
| 中文关键词: 亚纯函数, 分担函数, 正规族 |
| 英文关键词:Meromorphic functions, Shared functions, Normal families |
| 基金项目:本文受到国家自然科学基金 (No.11371149) 的资助. |
|
| Hits: 1312 |
| Download times: 580 |
| 中文摘要: |
| 设$k$为正整数, $M$为正数; $\mathcal{F}$为区域$D$内的亚纯函数族,
且其零点重级至少为$k$; $h$为$D$内的亚纯函数$(h(z)\not\equiv 0, \infty)$,
且$h(z)$的极点重级至多为$k$. 若对任意给定的函数$f \in \mathcal{F}$,
$f$与$f^{(k)}$分担$0$, 且$f^{(k)}(z)-h(z)=0\Rightarrow |f(z)|\geq M$,
则$\mathcal{F}$在$D$内正规. |
| 英文摘要: |
| Let $k$ be a positive integer, $M$ a positive number,
$\mathcal{F}$ a family of meromorphic functions in a domain $D$,
whose zeros are of mulitiplity at least $k$, and $h$ a
meromorphic function in $D \ (h(z)\not\equiv 0, \infty)$ and all
poles of $h(z)$ have multiplicity at most $k$. If for each function
$f\in \mathcal{F}$, $f$ and $f^{(k)}$ share 0, and
$f^{(k)}(z)-h(z)=0\Rightarrow |f(z)|\geq M$, then $\mathcal{F}$ is
normal in $D$. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
