UNIQUENESS AND ITS GENERALIZATION OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS

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 $E_k(1, f^nf^{(k)})=E_k(1,g^ng^{(k)}),$ where $k$ and $n$ are two positive integers satisfying $k\geq 3$ and $n\geq 2k+9,$ then either $f{(z)}=c_1e^{cz}, g{(z)}=c_2e^{-cz},$ where $c_1, c_2, c$ are three constants, satisfying $ (-1)^k (c_1c_2)^nc^{2k}=1.$