Some Results About Normal Family And Value Distribution Theory For Meromorphic Functions

This thesis is structured as follows. In Chapter 1, we provide background mate-rial about a few definitions and some well known results which will be used in this thesis, including normal families and value distribution theory. In Chapter 2, we pro-vide two results regarding normal families of holomorphic functions, which improve the normality criterion obtained by Xuecheng Pang, Mingliang Fang and Zalcman and are also a supplement for the result of Xiaojun Liu and Yasheng Ye. In Chapter 3, we obtain a new normality criterion concerning shared functions, which extends a recent result of Jianming Chang. In Chapter 4, by weakening some assumption of the existing normality criterion, we discuss the properties of the non-normal families and then obtain a new normality criterion. In Chapter 5, we use a new method to get two results of value distribution of meromorphic functions, which generalize Hay-man’s alternative and the related results of Xuecheng Pang, Pai Yang and Xiaojun Liu.