Uniqueness Of Meromorphic Functions Involving Derivatives

In this paper we study the uniqueness of meromorphic functions, which is an important subject in complex analysis. Much work was made on this respect. In the preface, we give a review about the historical background of complex analysis and research achievements in these fields. The present paper is divided into three parts.In chapter one, we state a few usual notations, definitions and basic results in value distribution theory of meromorphic function and unicity.In chapter two, we discuss the uniqueness of meromorphic functions concerning derivative, and prove the following theorem:Let f be a nonconstant meromorphic function whose poles have multiplicity n > 11 ; let a and b be two distinct finite complex numbers. If f and f' share a, b IM,then f = f'.In chapter three, we study the uniqueness of meromorphic functions concerning differential polynomial, and obtain the following result:Let f be a nonconstant meromorphic function satisfying N(r,f) <1/8n+17 T(r, f); let a(z) and b(z) be two distinct small functions related to f(z);and letF(z) = f(n)(z) + a1(z)f(n-1)(z) + ...+ an(z)/(z),where n is a positive integer and a1(z),a2(z), ...,an{z) are small functions related to f(z). If f(z) and F(z) share a(z) and b(z) CM almost .then f(z) = F(z).