亚纯函数的正规族与分担集

Normality and shared set of meromorphic functions

应用Zalcman-Pang引理,研究了涉及分担集的亚纯函数正规族,所得定理推广了林国斌与陈俊凡的结果.设F为区域D内的一族亚纯函数,h为有穷正数,k为正整数,S={b1,b2},其中b1,b2是2个互异有穷复数,若f∈F,f-bi(i=1,2)的零点重级至少为k,且满足(1)f和L(f)分担集合S,(2)当L(f)(z)∈S时,f(k+1)(z)≠0且|L′(f)(z)|≤h,则F在区域D内正规.

By using Zalcman-Pang Lemma, the normal family of mreomorphic functions concerning share set was studied. Moreover, the result extends those obtained by Lin and Chen. Let F be a family of meromorphic functions in a domain D,let h be a positive number,let k be a positive integer,let S= {b1 ,b2 } where b1 and b2 are two distinct finite complex numbers. If,for every f∈F,all zeros of f-bi are of multiplicity at least k for i=1,2,f and L（f） share the set S ,f^（k＋1） （z）≠0 and ｜L′（f）（z） ｜ ≤h when L（f）（z）∈ S, then F is normal in D.