In this paper, we study the uniqueness of entire function and its differential-difference operators. We prove the following result: let f be a transcendental entire function of finite order, let \(\eta \) be a non-zero complex number, \(n\ge 1, k\ge 0\) two integers and let a and b be two distinct finite complex numbers. If f and \((\Delta _{\eta }^{n}f)^{(k)}\) share a CM and share b IM, then \(f\equiv (\Delta _{\eta }^{n}f)^{(k)}\).

中文翻译：

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关于其微分-差分算子的整个函数的唯一性

在本文中，我们研究了整个函数的唯一性及其微分差分算子。我们证明以下结果：设f为有限阶超越整函数，设\(\eta \)为非零复数，\(n\ge 1, k\ge 0\)两个整数，令a和b是两个不同的有限复数。如果f和\((\Delta _{\eta }^{n}f)^{(k)}\)共享一个CM 并共享b 个IM，那么\(f\equiv (\Delta _{\eta }^ {n}f)^{(k)}\)。