正规族与分担值  

Normality and Shared Values

作　　者：王永军[1] 郑丽 

机构地区：[1]重庆大学数学系,重庆400044 [2]阜阳大学,安徽阜阳236029

出　　处：《山西师范大学学报（自然科学版）》2007年第3期14-17,共4页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：本文研究正规族与分担值之间的关系,得到如下结果:设F是区域D内的亚纯函数族,a,b∈■,a,b≠1,若f∈F,f和f′在D内分担1,f=a■ f′=b,则F在D内正规;设F是区域D内的全纯函数族,k∈+,b∈+,b∈+,若f∈F,f-1的零点重级均≥k,f=1■ f(k)=1,f(k)=1■0<|f(k+1)|≤b,则F在D内正规.In this paper, the authors draw a connection between normal family and sharing values. They obtain the following nor-real criterions ： Let F be a family of meromorphic functions defined in a domain D,a,b∈C,a,b≠1,IF Af∈F f and f′share the value 1 in D f =a→f′=b,then F is normal in D. Let F be a family of holomorphic functions defined in a domain D,K∈N^＋,b∈R^＋,If Af∈F,the zeros f-1 are of multiplicity ≥k f=1→f^（k）=1f^（k）=1→0〈1f^（k＋1）1≤b,Then F is normal in D.

关 键 词：亚纯函数 全纯函数 正规族 分担值 

分 类 号：O174.52[理学—数学]