The present study introduces generalized -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of to with respect to values.

中文翻译：

---

广义-Bernstein–Stancu型算子的逼近性质

本研究介绍推广-伯恩斯坦-斯坦型运营商转向节。给出了Korovkin型逼近定理，并为Lipschitz型函数获得了这些类型算子的收敛速度。然后，针对这些算子的渐近行为给出了Voronovskaja型定理。最后，通过数值算例及其图形说明了收敛性。到相对于值。