It is a known uniqueness result that if f is a transcendental meromorphic function of finite order with two Borel excetional values \(a \ne \infty , b\) and its first order difference operator \({\triangle }_c f\not \equiv 0\), for some complex number c, and if f and \({\triangle }_c f\) share a, b CM, then \(a=0, b=\infty \) and \(f=\exp (Az+B)\), where \(A\ne 0, B \in {\mathbb {C}} \). This type of results has its origin dating back to Csillag-Tumura’s uniqueness theorems. In this paper, by using completely different methods, we shall show that the result holds for arbitrary higher order difference operators. Examples are provided to show that this result is not valid for meromorphic functions with infinite order, which also shows a distinction between the derivatives and the difference operators of meromorphic functions, in view of Csillag-Tumura type uniqueness theorems.

已知唯一性结果是，如果f是具有两个Borel激进值\（a \ ne \ infty，b \）及其一阶差分算子\（{\ triangle} _c f \ not \ equiv 0 \），对于某些复数c，如果f和\（{\ triangle} _c f \）共享a，  b CM，则\（a = 0，b = \ infty \）和\（f = \ exp（Az + B）\），其中\（A \ ne 0，B \ in {\ mathbb {C}} \）。这种类型的结果的起源可以追溯到Csillag-Tumura的唯一性定理。在本文中，通过使用完全不同的方法，我们将证明结果适用于任意高阶差分算子。提供的示例表明该结果对于具有无限阶的亚纯函数无效，并且鉴于Csillag-Tumura型唯一性定理，这也表明了亚纯函数的导数和差算符之间的区别。