Several Results On The Normal Family Of Meromorphic Functions And Normal Functions

The theory of normal families is an important and classical branch of the complex analysis.Much work has been taken on this issue.In this thesis,we mainly study normal families,quasinormal families and normal functions.The dissertation is arranged as following:In preface,we briefly review the development background and some research achievements of the theory of normal family.In Chapter 1,we introduce some basic knowledge in value distribution theory,normal family and quasinormal families.In Chapter 2,we extend the normal criteria of meromorphic functions concerning coefficient fuction of Yang-Yang-Pang [8] and Yang-Pang [9] from analytic functions to more general meromorphic functions and obtain several theorems.In Chapter 3,we study the normal criteria of meromorphic functions concerning differential polynomials,which generalizes the related results due to Zhang [13].In Chapter 4,we study the properties of quasinormality and generalize the corresponding results of Yang-Hu-Pang [17].In Chapter 5,we study the five-point theorems of normal functions and obtain a more general five-value theorem about ?-normal functions,which extends the related results due to Xu [26].