The Growth Of A Class Of Composite Entire Functions And Meromorphic Functions

In this paper,we use some basic knowledge of the value distribution theo-ry of entire functions and meromorphic functions.We investigate the growth of composite entire functin f(g):which mainly includes the iterated type and the iterated lower type,the relative hyper-order and the relative hyper-type of com-posite function f(g)relative to entire function h(z).We also compare the growth of the maximum modulus M(r,f(g))of composite function f(g)with the max-imum modulus M(r,g)of entire function g(z).’ The thesis is divided into three chapters.In chapter 1,we introduce some basic definitions,properties and usual nota-tions of entire functions and meromorphic functions.In chapter 2,we study the iterated order and iterated type of composite entire function f(g)when f(z)and g(z)are entire functions of finite iterated order and satisfy certain conditions.We also estimate the rate by comparing the growth of logp+q M(r,f(g))with that of logq M(r,g).Some results are improved and generalized.In chapter 3,we study the the relative hyper-order and the relative hyper-type of composite function f(g)when the relative order of the outer function f(z)and the growth order and type of the inner function g(z)satisfy certain conditions,we obtain some results which generalize and improve some previous results.