The Problems About Normality And Value-sharing Of Meromophic Function

In1925, R.Nevanlinna developed two basic theorems of meromorphic functions,and then created modern research of the value distribution theory. In resent severaldecades,people used the value distribution to resolve many problems on the normalityof meromorphic functions and obtain lots of profound results. The paper is based onthe theorems which people had built. Shared values and normality of meromorphicfunctions is studied, and we obtain some corresponding results. Also the whole paperis divided four chapters.The first chapter of the paper is about preliminary theory. We mainly introducethe background of the paper, the main content of Nevanlinna’s theory, the normalityof meromorphic function, relational signs and fundamental theory.In the second chapter, we discusses fn(z)f(k)(z)=a=|f(k)(z)|≤b, f(k)(z)=c=|fn(z)f(k)(z)|≥d, this condition is satisfied the normality of meromorphicfunctions, we obtain a correlation result.In the third chapter, we mainly discusses f(z)=a f(k)(z)=b,f(k)(z)=c f(k+1)(z)=d and f(z)=a f(k)(z)=b, and for any of the z∈D, f(k)(z)=c,f(k+1)(z)=d, the two conditions are satisfied the normality of meromorphic functions,which is a generalization and improvement of Jianming.Chang, Xiaojie.Huang etc.In the fourth chapter, we mainly concerns f afnandg agn, we study normalityof meromorphic functions of sharing the fixed point z, n is respectively1,2,3. Severalrelated results are obtained.