与分担值相关的亚纯函数的正规性-重庆师范大学学报（自然科学版）

文章信息/Info

Author(s):: RUAN Jie-chang1; 2; SHAO Wen-kai2; GU Yong-Xing1; 1. College of Mathematics and Physics, Chongqing University, Chongqing 400030;
2. Basic Education Department, Yibin Vocational & Technical College, Yibin Sichuan 644003, China

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=a f=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=a f=b和f≠0，则F在D内正规。

Abstract:: 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, 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 get the following two theorems: Let F be a family of meromorphic functions in a area D, a(≠0) and b(≠0)are two limited complex numbers, if f∈F, f ′f=a f=b, then F is normal . Let F be a family of meromorphic functions in a area D, a(≠0) and b(≠0) are two limited complex numbers, if f∈F, f (k)f=a f=b and f≠0, then is normal.