Uniqueness on Meromorphic function concerning their differential-difference operators

In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of ${\rho }_2(f)<1$, let $\eta$ be a non-zero complex number, $n\ge 1,k\ge 0$ two integers and let $a\equiv ̸0,\mathrm{\infty }$ be a small function of $f$. If $f$ and $({\mathrm{\Delta }}_{\eta }^{n}f{)}^{(k)}$ share $0,\mathrm{\infty }$ CM and share $a$ IM, then $f\equiv ({\mathrm{\Delta }}_{\eta }^{n}f{)}^{(k)}$, which use a completely different method to improve some results due to Chen-Xu [1].