全纯函数的正规族与分担集

The Normal Family and Sharing Set of Holomorphic Functions

利用分担集合的思想证明了定理:设F是单位圆盘内的一族全纯函数族,a1和a2是2个不同的有限复数且a1+a2≠0;当α≥1时,如果对于任意的f∈F,Ef(S)=E f′(S),S={a 1,a2}在单位圆内成立,那么f是一个α-正规函数.

In this paper, the idea of the sharing set was used to prove the following theorem： Let F be a family of holomorphic functions in the unit disc, a1 and a2 be two distinct finite numbers with a1＋a2≠0. If α≥1, forany f∈F,Ef（S）=Ef′（S）, S={a1,a2} in the unit disc, then f is an α- normal function.