涉及分担集合的亚纯函数正规族  

Normal Families of Meromorphic Functions Involving Shared Sets

作　　者：冉娜 饶梓骞 杨祺[1] RAN Na;RAO Zi-qian;YANG Qi(Institute Of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China;College of Computer Science and Engineering,Southeast University,Nanjing 211102,China)

机构地区：[1]新疆师范大学数学科学学院 [2]东南大学计算机科学与工程学院

出　　处：《宜春学院学报》2023年第12期6-8,30,共4页Journal of Yichun University

基　　金：国家自然科学基金项目(编号:11961068)。

摘　　要：本文是在2023年李丹等人在文[4]中的定理A和定理B基础上进行了改进,将f^((k))(z)推广到关于f的微分多项式L(f),使条件更加一般化,推广了已有的结论,并通过反证法,结合Zaclman-Pang引理,利用构造辅助函数的方式,分情况讨论并证明了涉及分担集合的正规定则。首先,考虑了双向分担集合情形,得到了:当f(z)∈S_(1)■L(f)(z)∈S_(2)时,则亚纯函数族F在区域D上是正规的;其次,减弱了条件,得到了:若f(z)∈S_(1)?L(f)(z)∈S_(2),则F在区域D上正规;最后,将条件再一次进行推广,得到了:若f(z)∈S_(1)■|L(f)(z)|≤M,则F在区域D上正规。This article is an improvement on Theorem A and Theorem B proposed by Li Dan et al.in^([4])in 2023,by extending f^((k))(z) to differential polynomials related to f of L(f),making the conditions more general and generalizing existing conclusions.Through the method of proof to the contrary,combined with the Zaclman Ping lemma,and using the construction of auxiliary functions,we discuss and prove the normal rule involving shared sets in different cases.Firstly,we consider the case of bidirectional shared sets and obtain:When f(z)∈S_1■L(f)(z)∈S_2,then the family of meromorphic functions F is normal in the domain D.Secondly,weakened the condition,obtained:if f(z)∈S_1■L(f)(z)∈S_2,then F is normal in the domain D.Finally,extended the condition again,obtained:if f(z)∈S_1?|L(f)(z)|≤M,then F is normal in the domain D.

关 键 词：亚纯函数 正规族 微分多项式 分担集合 

分 类 号：O174.52[理学—数学]