Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1598-1605.

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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
  • Received:2020-06-11 Online:2021-12-26 Published:2021-12-02
  • Contact: Daochun Sun;;
  • Supported by:
    the NSFC(11501127);the Guangzhou Civil Aviation College(18X0428)


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.

Key words: Meromorphic functions, Normal family, Covering surface, Island, Discrete values of one Leaf

CLC Number: 

  • O174.52