涉及分担函数与分担值的正规定则  

Normal Criterion Concerning Shared Functions and Shared Values

作　　者：曾翠萍[1] 邓炳茂 方明亮[2] ZENG Cuiping;DENG Bingmao;FANG Mingliang(Department of Applied Mathematics,Guangdong University Of Finance,Guangzhou 510521,China;Corresponding author.Department of Applied Mathematics,Guangdong University Of Finance,Guangzhou 510521,China;Institute of Applied Mathematics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]广东金融学院应用数学系,广州510521 [2]华南农业大学应用数学研究所,广州510642

出　　处：《数学年刊（A辑）》2021年第1期115-124,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11901119);广东省普通高校特色创新类项目(No.2019KTSCX111)的资助。

摘　　要：研究了涉及分担函数的正规定则,证明了:设F为定义在区域D内的一族亚纯函数,n,k是两个正整数,满足n≥k+3.如果对于F中任意一个函数f,(f^(n))^(((k)))-z至多有一个不同的零点,则F在D内正规.此结论说明在(f^(n))^(((k)))具有不动点的情形下,1990年杨乐在Notre Dame大学举行的学术会议上提出的断言仍然成立.The authors study normal criterion concerning share functions and share values and prove:Let F be a family of meromorphic functions in D,and let k,n be two positive integers with n≥k+3.For each f∈F,(f^(n))^((k))-z has at most one zero,then F is normal in D.It means that the claim made by Yang at the academic conference in University of Notre Dame in 1990 is still valid when(f^(n))^((k))has fixed point.

关 键 词：亚纯函数 正规族 分担函数 分担值 

分 类 号：O174.52[理学—数学]