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
收藏
页数：17
相关论文
共 50 条
12345