• 论文 •

### 亚纯函数关于单叶离散值的正规定理

1. 1 广东培正学院数据科学与计算机学院 广州 510830
2 广东金融学院金融数学与统计学院 广州 510521
3 华南师范大学数学科学学院 广州 510631
• 收稿日期:2020-06-11 出版日期:2021-12-26 发布日期:2021-12-02
• 通讯作者: 孙道椿 E-mail:betty0104@sina.com;chaifujie@sina.com;1457330943@qq.com
• 作者简介:郭晓晶, E-mail: betty0104@sina.com|柴富杰, E-mail: chaifujie@sina.com
• 基金资助:
国家自然科学基金(11501127);广州民航学院基金(18X0428)

### Normal Family Theorems for Meromorphic Functions with Discrete Values of One Leaf

Xiaojing Guo1(),Fujie Chai2(),Daochun Sun3,*()

1. 1 School of Data Science and Computer Science, Guangdong Peizheng College, Guangzhou 510830
2 School of Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521
3 School of Mathematics Science, South China Normal University, Guangzhou 510631
• Contact: Daochun Sun E-mail:betty0104@sina.com;chaifujie@sina.com;1457330943@qq.com
• Supported by:
the NSFC(11501127);the Guangzhou Civil Aviation College(18X0428)

Abstract:

In this paper, the normal theorems of meromorphic functions involving discrete values are studied by using the theory of Ahlfors covering surfaces. Firstly, the discrete values with one leaf of meromorphic functions are defined, then the inequalities about islands are investigated and two precise inequalities about islands are obtained. Finally, the inequalities are used to study the discrete values and the normal family of meromorphic functions, then a normal theorem involving a monophyletic island and a normal theorem involving discrete values of one leaf are obtained. All these theorems promote the famous Ahlfors' five islands theorem and five single valued theorem of Nevanlinna.

• O174.52