A new proof of entire function sharing three small functions CM with it $n-$ exact difference

In this paper, we study the uniqueness of the difference of meromorphic functions. We give a new proof of the following result: Let $f$ be a transcendental meromorphic function of hyper-order less than $1$, let $eta$ be a non-zero complex number, $ngeq1$, an integer, and let $a,b,c$ be three distinct periodic small functions with period $eta$. If $f$ and $Delta_{eta}^{n}f$ share $a,b,c$ CM, then $fequivDelta_{eta}^{n}f$, which using a different method from cite{gkzz}.