The current paper deals with the parametric modification of Meyer-König-Zeller operators which preserve constant and Korovkin’s other test functions in the form of ${\left(\frac{x}{1-x}\right)}^u$, $u=1,2$ in limit case. The uniform convergence of the newly defined operators is investigated. The rate of convergence is studied by means of the modulus of continuity and by the help of Peetre-$\mathcal{K}$ functionals. Also, a Voronovskaya type asymptotic formula is given. Finally, some numerical examples are illustrated to show the effectiveness of the newly constructed operators for computing the approximation of function.

中文翻译：

---

Meyer-König-Zeller 算子的参数化推广

当前论文涉及 Meyer-König-Zeller 算子的参数修改，这些算子以以下形式保留常数和 Korovkin 的其他测试函数 ${\left(\frac{X}{1-X}\right)}^{你}$, $你=1,2$在极限情况下。研究了新定义算子的一致收敛性。收敛速度是通过连续性模数和 Peetre 的帮助来研究的$\mathcal{钾}$泛函。此外，还给出了 Voronovskaya 型渐近公式。最后，通过一些数值例子说明了新构造的算子在计算函数逼近中的有效性。