Abstract
In this paper, we study the unicity of meromorphic functions concerning higher order difference operators and mainly prove the following result: Let \(m,n(\geq 6)\) be positive integers, let \(\eta\) be a nonzero complex number, and let \(f\) be a nonconstant meromorphic function in the complex plane. If \(f^{n}\) and \((\Delta^{m}_{\eta}f)^{n}\) share \(1\) CM, \(f\) and \(\Delta^{m}_{\eta}f\) share \(\infty\) IM, then \(\Delta^{m}_{\eta}f\equiv tf\) , where \(t^{n}=1\) , and if \(m=1\) , then \(t\not=-1\) . This improves the results due to Chen and Chen [Bull. Malays. Math. Sci. Soc. 35 (2012)] and Deng, Liu and Yang [Turkish J. Math. 41 (2017)] for the case of infinite order and higher order difference operators.
