分担值与亚纯函数的正规族

本文通过定义R1={f1=f-c;f∈R},将R在Δ上的正规转换为研究R1在Δ上的正规。运用文献8]得到R1在Δ 不正规的充分必要条件：存在点列zj∈Δ,函数列f1j∈R1和正数列ρj→0＋ ,使得gj（ξ）=f1j（zj＋ρjξ）→g（ξ）,并且g（ξ）是非常数亚纯函数,再运用分担值的定义和文献9]中的不等式得到g（ξ）又必为一个常数,通过反证推广了陈怀惠和方明亮的结果。设R是区域D 上的一族亚纯函数,k是一不小于2的正整数,a,b,c是有穷复数,a≠b,如果对任意的f∈R,f-c的零点重级至少是k,并且f和f（k）在D 分担a 与b,则R在D 上正规。

Sharing Values and the Normal Family of Meromorphic Functions

In this paper, defining R1={f1=f-c;f∈R},Then Rt is normal in △ if and only R1 is normal in △. By using the literature 8] to get a necessary and sufficient condition which R1 iS not normal in A： there exist complex points zj∈Δ, functionsf1j∈R1 and positive numbers ρj→0＋, such that gj（ξ）=f1j（zj＋ρjξ）→g（ξ）,where g（ξ）is nonconstant. And then by using the definition of shared values and the literature 9] get g（ξ） shall be a constant, that is a contradiction, promoting the results of Chen Huai-hui and Fang Ming-liang. Let R be a family of mermorphic functions in a domain D, let k≥2 be a positive integer, and a, b, c be distinct complex numbers. If for each f∈Rthe zeros of f （z） -c are of multiplicit y≥k, and ^-Ef （a） =^1Ef（k） （a）,^Ef（b）=^Ef（k）（b）,then R is normal in D.