与分担值相关的亚纯函数的正规性  

Normal Families and Shared Values of Meromorphic Functions

作　　者：阮杰昌[1,2] 邵文凯[2] 顾永兴[1] 

机构地区：[1]重庆大学数理学院,重庆400030 [2]宜宾职业技术学院基础部,四川宜宾644004

出　　处：《重庆师范大学学报（自然科学版）》2009年第2期61-62,78,共3页Journal of Chongqing Normal University:Natural Science

基　　金：宜宾职业技术学院科研项目(No.200701)

摘　　要：正规性是单复变函数中的一个重要研究课题,本文主要研究亚纯函数的正规性问题。运用了Zalcman引理和正规族的相关理论,研究了与分担值相关的亚纯函数的正规性问题,得到了与分担值相关的结论:设F是区域D内的亚纯函数族,a(≠0)与b(≠0)是两个有穷复数,若对F中的任意函数f,有f′f=af=b,则F在D内正规;设F是区域D内的亚纯函数族,k是一正整数,a(≠0)与b(≠0)是两个有穷复数,若对F中的任意函数f,有f(k)f=af=b和f≠0,则F在D内正规。In recent years, normal families with sharing values has been becoming an activated subject. Much work was made on this respect by using mainly the Navelinna＇ s value distribution theory and the theory of normal families of mermorphic functions. A series of normality criteria are attained, such as the normality criterion concerning sharing sets, sharing a value and sharing functions. In this paper, we do a further study in normal families of mermorphic functions on sharing values, which is an important subject in complex analysis. We have got the two following theorems. Let F be a family of meromorphic functions in a area D, a（≠0） and b（≠0） are two limited complex numbers, if arbitary ∈F, f′f= a→f= b, then F is normal. Let F be a family of meromorphie functions in a area D, a （≠0） and b（≠0） are two limited complex numbers, if arbitary ∈ F,f^（k）f= a→f= b and f≠0, then F is normal.

关 键 词：亚纯函数 正规定则 分担值 

分 类 号：O174.52[理学—数学]