A new approach to improve the order of approximation of the Bernstein operators: theory and applications

被引：38

作者：

Khosravian-Arab, Hassan ^{[1
]}

Dehghan, Mehdi ^{[1
]}

Eslahchi, M. R. ^{[2
]}

机构：

[1] Amirkabir Univ Technol, Fac Math Comp Sci, Dept Appl Math, 424 Hafez Ave, Tehran, Iran

[2] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, POB 14115-134, Tehran, Iran

来源：

NUMERICAL ALGORITHMS | 2018年 / 77卷 / 01期

关键词：

Linear positive operator; The Bernstein operators; Bernstein Theorem; Korovkin Theorem; Voronovkaja Theorem; Rate of convergence; Degree of convergence; ASYMPTOTIC-EXPANSION;

D O I：

10.1007/s11075-017-0307-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically.

引用

页码：111 / 150

页数：40

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