Uniqueness and its generalization of meromorphic function concerning differential polynomials

Abstract

Considering the generalization of uniqueness of meromorphic functions of differential monomials, we obtain that if two non-constant meromorphic functions f(z) and g(z) satisfy Ek(1, fnf(k) ) = Ek(1, gng(k) ), where k and n are two positive integers satisfying k ≥ 3 and n ≥ 2k+9, then either f(z) = c1ecz, g(z) = c2e−cz, where c1, c2, c are three constants, satisfying (−1)k(c1c2)nc2k = 1.