分担一个亚纯函数的亚纯函数族的正规定则

Normality Criteria of Meromorphic Functions Sharing a Meromorphic Function

中文关键词:  亚纯函数  分担值  正规定则.

英文关键词:meromorphic function  shared values  normality criteria.

中文摘要:

      设$\mathcal{F}$是区域$D$内的一族亚纯函数, $\psi(\neq 0)$是区域$D$内的一个只有单级极点的亚纯函数,并假设对于任意的$f\in\mathcal{F}$,在区域$D$内$f\neq 0$.如果对于任意一对$\{f,\,g\}\subset\mathcal{F}$, $f'$和$g'$在区域$D$内分担$\psi$,那么$\mathcal{F}$在区域$D$内正规.

英文摘要:

      Let $\mathcal{F}$ be a family of meromorphic functions in $D$, and let $\psi(\neq 0)$ be a meromorphic function in $D$ all of whose poles are simple. Suppose that, for each $f\in\mathcal{F}$, $f\neq 0$ in $D$. If for each pair of functions $\{f,\,g\}\subset\mathcal{F}$, $f'$ and $g'$ share $\psi$ in $D$, then $\mathcal{F}$ is normal in $D$.