Modified α-Bernstein-Durrmeyer-Type Operators

被引：0

作者：

Agrawal, P. N. ^{[1
]}

Kajla, Arun ^{[2
]}

Singh, Sompal ^{[1
]}

机构：

[1] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, Uttar Pradesh, India

[2] Cent Univ Haryana, Dept Math, Jant 123031, Haryana, India

来源：

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE | 2021年 / 45卷 / 06期

关键词：

Peetre's K-functional; Ditzian-Totik modulus of smoothness; Voronovskaja-type theorem; Gruss Voronovskaja-type theorem; Functions of bounded variation; APPROXIMATION PROPERTIES; POLYNOMIALS; CONVERGENCE; DERIVATIVES; THEOREM;

D O I：

10.1007/s40995-021-01197-y

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we construct a Durrmeyer variant of the modified alpha-Bernstein-type operators introduced by Kajla and Acar (Ann Funct Anal 10(4):570-582, 2019), for alpha is an element of[0,1]. We investigate the degree of approximation via the approach of Peetre's K-functional and the Lipschitz-type maximal function. The quantitative Voronovskaja- and Gruss Voronovskaja-type theorems are discussed. Further, we determine the rate of convergence by the above operators for the functions with derivatives of bounded variation.

引用

页码：2049 / 2061

页数：13

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