具有实参数移位结点的q-Bernstein-Stancu-Kantorovich算子在Orlicz空间内的逼近

Approximation of the q-Bernstein-Stancu-Kantorovich Operator with Real-parameter Shifted Knots in Orlicz Space

本文研究了q-Bernstein-Stancu-Kantorovich算子在Orlicz空间内的逼近问题,利用鲁津定理首先给出了简单的q-Bernstein-Stancu-Kantorovich算子的收敛性定理;在此基础上,借助Hölder不等式、光滑模和K泛函等工具研究了较复杂的q-Bernstein-Stancu-Kantorovich算子在Orlicz空间内的逼近性能,给出了逼近阶的估计。

In the paper,the approximation problem of the q-Bernstein-Stancu-Kantorovich operator in the Orlicz space was studied,and the convergence theorem of the simple q-Bernstein-Stancu-Kantorovich operator was first given by using the Luzin theorem.On this basis,the approximation performance of the complex q-Bernstein-Stancu-Kantorovich operator in the Orlicz space was studied with the tools such as the Hölder’s inequality,smooth mode and K-functional.Finally,the approximation order is estimated.