摘要
如果亚纯函数族中的函数与其导数分担含有至少3个元素的有限集合则该函数族必定正规,而分担含有无限个元素的集合函数族通常并不正规。在附加约束的条件下证明了一个分担无限集合的亚纯函数族正规定则。设F是区域D上的一族亚纯函数,S是一个有界无限复数集且含有至少3个孤立点,如果在区域D上,对每个f∈F,有f∈S■f'∈S,则F在区域D上正规。根据进一步的分析,本文猜测若将前述“S有界”的条件改为“S与原点的距离大于0,即dist(S,0)>0”,F仍然正规。
A family of meromorphic functions must be normal if every function in the family shares afinite set of at least 3 elements with its derivatives,whereas a family of meromorphic functions that shares a set of infinite number of elements is usually not normal.In this paper,we prove a normal criterion of family of meromorphic functions for sharing infinite set under some additional constraints.Let F be a family of meromorphic functions on a region D,S be a bounded infinite set of complex numbers with at least 3 isolated points,if on the region D,for each f∈F,there isf∈S■f'∈S,then F is normal on the region D.Based on further analysis,this paper speculates that if the aforementioned"bounded"condition of S is changed to"the distance between S and the origin is greater than 0,that is dist(,0)0S>",then F will still be normal.
作者
黄小杰
李运通
费荔枝
HUANG Xiaojie;LI Yuntong;FEI Lizhi(Department of Science,Nanchang Institute of Technology,Nanchang 330099,China;Key Laboratory of Engineering Mathematics and Advanced Computing,Nanchang Institute of Technology,Nanchang 330099,China;Department of Basic Course,Shaanxi Railway Institute,Weinan 714025,China)
出处
《南昌大学学报（理科版）》
CAS
2024年第5期416-420,共5页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(12461014)
陕西铁路工程职业技术学院科研基金项目(KY2019-46)
江西省教育厅科学技术研究项目(GJJ211926)。
关键词
亚纯函数
正规族
分担集合
meromorphic function
normal family
shared set
