In the present paper, q-analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a Voronovskaja type theorem and local approximation results for the said operators are studied. Error estimation tables are presented with respect to different parameters. We also show comparisons by some illustrative graphics for the convergence of operators to a function with the help of MATLAB R2018a.

中文翻译：

---

q-Bernstein位移算子的逼近性质和误差估计

在本文中，介绍了带有移位结的LupaşBernstein算子的q模拟。首先，建立了引入算子收敛的一些基本结果，然后获得了这些算子在连续模数方面的收敛速度。此外，研究了Voronovskaja型定理和所述算子的局部近似结果。给出了关于不同参数的误差估计表。我们还通过一些说明性的图形进行了比较，以借助MATLAB R2018a帮助运算符收敛到函数。