一个正规定则的推广

证明了如下结果:设F是区域D内的一族亚纯函数,k≠2是正整数,c,d为两个非零有穷复数.a(z)是一个在D内不取零值的全纯函数.若对每一个f∈F,f的零点重级k,若f(z)=0则f(k)(z)=a(z),f(k)(z)=a(z)则|f(k+1)(z)|h,(h为某一正数),f(z)=c则f′(z)=d,则F在D内正规.

Generalization of a Normal Criterion

In this paper it has been generalized that a normality and prove the following result.Let F be a family of mermorphic functions in a domain D,all of whose zeros are of multiplicity at least k.Let k≠2 be a positive integer,c,d be two nonzero finite complex numbers,a(z) be a function holomorphic in D such that a(z)≠0 for z∈D.If for any f∈F,f(z)=0 detrude f(k)(z)=a(z),f(k)(z)=a(z) detrude |f(k)(z)|h(h is a positive number,f(z)=c detrude f′(z)=d,then F is normal in D.