Recently, some uniqueness theorems about meromorphic functions f(z) concerning their derivatives \(f'(z)\) and shifts \(f(z+c)\) with three CM sharing values have been obtained. In this paper, we continue to study this topic. We consider not only high order derivatives instead of just \(f'(z)\), but also IM sharing value instead of CM sharing value. In fact, we mainly prove that for a non-constant meromorphic function f(z) of hyper order strictly less than 1, if \(f^{(k)}(z)\) and \(f(z+c)\) share \(0,\infty \) CM and 1 IM, then \(f^{(k)}(z)\equiv f(z+c)\), where c is a non-zero finite complex number. Our main theorem generalizes and greatly improves the related result due to Qi–Li–Yang. In addition, we give some discussion of this issue and obtain a uniqueness theorem concerning defective values in Sect. 3.

最近，已经获得了关于亚纯函数f（z）的导数\（f'（z）\）和具有三个CM共享值的移位\（f（z + c）\）的唯一性定理。在本文中，我们将继续研究该主题。我们不仅考虑高阶导数而不只是\（f'（z）\），还考虑IM共享值而不是CM共享值。事实上，我们主要证明，对于非恒定亚纯函数˚F（ž超量级）比1严格较少，如果\（F ^ {（K）}（Z）\）和\（F（Z + C） \）共享\（0，\ infty \） CM和1 IM，然后\（f ^ {（k）}（z）\ equiv f（z + c）\），其中c是非零的有限复数。我们的主要定理推广并大大改善了由于齐立阳所导致的相关结果。此外，我们对此问题进行了一些讨论，并获得了有关Sect中缺陷值的唯一性定理。3。