Estimation Of The Growth Of A Series Of Composite Functions

In this paper,we use the knowledge of Nevanlinna value distribution theory combined with difference and q difference to estimate the growth of the composite function f(Δng),(Δf)(g),f(Δqng).When f(z)is entire or meromorphic function of finite logarithm iterated order and g(z)is an entire function of finite order.We also investigate the growth of composite function f(g(z)).This thesis is divided into three chapters.In chapter 1,we introduce some basic definitions and symbols of entire func-tions and meromorphic functions,the Nevanlinna value distribution theory and some relative theorems.In chapter 2,we introduce the definition of nth order difference and q differ-ence of the entire function f(z).Three important properties are given,and then we compared the growth of composite function f(Δng),(Δf)(g),f(Δqng)and get some estimations.In chapter 3,we introduce some definitions of entire functions of finite loga-rithmic iteration order.In addition,when f(z)is an entire or meromorphic function of finite logarithmic iteration order and g(z)is an entire function,the order and type,zero and pole convergence exponent of the composite function f(g(z))are estimated.Also,some previous conclusions are improved and extended.