Abstract

In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Grüss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.

摘要

在本文中，我们介绍了n 次Bernstein-Kantorovich-Stancu 类型算子的新扩展在多个形状参数的帮助下。Voronovskaja 和 Grüss-Voronovskaja 类型逼近定理通过 Ditzian-Totik 平滑模量进行检验。我们研究了关于非负正则可和矩阵的基本统计收敛特性。此外，使用 Ditzian-Totik 模数，已经建立了与所建议的算子相关联的局部和全局近似属性。最后，给出了几个说明性的例子来证明算子的效率、适用性和有效性。图形和数值结果验证了所提出的算子提供了更好的近似值，并扩展了先前的 Bernstein-Kantorovich 类型修改，包括单个参数。