Approximation Properties of the Blending-Type Bernstein-Durrmeyer Operators

被引：2

作者：

Liu, Yu-Jie ^{[1
]}

Cheng, Wen-Tao ^{[1
]}

Zhang, Wen-Hui ^{[2
,3
]}

Ye, Pei-Xin ^{[2
,3
]}

机构：

[1] Anqing Normal Univ, Sch Math & Phys, Anqing 246133, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

AXIOMS | 2023年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

modified Bernstein-Durrmeyer operators; Voronovskaya-type theorem; local approximation; global approximation; K-functional; modulus of smoothness; bounded variation;

D O I：

10.3390/axioms12010005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct the blending-type modified Bernstein-Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and K-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.

引用

页数：17

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