On the rate of convergence of two generalized Bernstein type operators

被引：1

作者：

Lian, Bo-yong ^{[1
]}

Cai, Qing-bo ^{[2
]}

机构：

[1] Yang En Univ, Dept Math, Quanzhou 362014, Peoples R China

[2] Quanzhou Normal Univ, Sch Math & Comp Sci, Quanzhou 362000, Peoples R China

来源：

APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2020年 / 35卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Bernstein operators; modulus of smoothness; rate of convergence; bounded variation; BLENDING TYPE APPROXIMATION; BEZIER VARIANT; POLYNOMIALS;

D O I：

10.1007/s11766-020-3610-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the Bezier variant of two new families of generalized Bernstein type operators. We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity. By means of construction of suitable functions and the method of Bojanic and Cheng, we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.

引用

页码：321 / 331

页数：11

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