华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (1): 54-60, 75.

• 应用数学与基础数学 • 上一篇    下一篇

与分担值相关的正规族

李三华,  刘忠东,  吴高翔   

  1. 井冈山大学~~数理学院, 江西~~吉安 343009
  • 收稿日期:2011-11-01 修回日期:2012-02-01 出版日期:2013-01-25 发布日期:2013-01-18

Normal families related to shared values

LI San-hua, LIU Zhong-dong, WU Gao-xiang   

  1. College of Mathematics and Physics, Jinggangshan University, Jian Jiangxi 343009, China
  • Received:2011-11-01 Revised:2012-02-01 Online:2013-01-25 Published:2013-01-18

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摘要： 设\,$\F$\,为区域\,$D$\,上的亚纯函数族,
$a$\,和\,$b$\,都是不为零的两个有穷复数($\frac{a}{b}$\,不是正整数),
若每个\,$f \in \F$, $f(z) = a \Rightarrow f^{(k)}(z) = a$, 且\,$f -
a$\,的零点重级至少为\,$k$, 当\,$f^{(k)}(z) = b$\,时有\,$|f(z) - a|
\geq \varepsilon$, 其中\,$\varepsilon$\,为正数.
则\,$\F$\,在区域\,$D$\,内正规.

关键词: 亚纯函数, 零点, 正规族

Abstract: Let $\F$ be a family of meromorphic functions on a domain
$D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$
not positive integer). If for every $f \in \F$, $f(z) = a
\Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$
is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon >
0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.

Key words: meromorphic function, zero point, normality

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