Iterated Boolean Sums of Bernstein Type Operators

被引：4

作者：

Acar, Tuncer ^{[1
]}

Aral, Ali ^{[2
]}

Rasa, Ioan ^{[3
]}

机构：

[1] Selcuk Univ, Fac Sci, Dept Math, TR-42003 Selcuklu, Konya, Turkey

[2] Kirikkale Univ, Fac Arts & Sci, Dept Math, Kirikkale, Turkey

[3] Tech Univ Cluj Napoca, Cluj Napoca, Romania

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2020年 / 41卷 / 12期

关键词：

Bernstein polynomials; Boolean sums; iterated operators; LINEAR-COMBINATIONS; EIGENSTRUCTURE; APPROXIMATION; LAGRANGE; LIMITS;

D O I：

10.1080/01630563.2020.1777160

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative and quantitative results concerning the approximation by such Boolean sums. The general results are illustrated by examples.

引用

页码：1515 / 1527

页数：13

共 32 条

[1] On the iterates of some Bernstein-type operators [J].

Adell, JA ;

Badia, FG ;

delaCal, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 209 (02) :529-541

[2]

Agrawal P. N., 1984, Demonstr. Math., V17, P777

[3]

[Anonymous], 1973, Journal of Approximation Theory

[4] Convergence of Iterated Boolean-type Sums and Their Iterates [J].

Campiti, Michele .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (10) :1054-1063

[5] STRONG CONVERSE INEQUALITY FOR THE BERNSTEIN-DURRMEYER OPERATOR [J].

CHEN, W ;

DITZIAN, Z ;

IVANOV, K .

JOURNAL OF APPROXIMATION THEORY, 1993, 75 (01) :25-43

[6] The eigenstructure of the Bernstein operator [J].

Cooper, S ;

Waldron, S .

JOURNAL OF APPROXIMATION THEORY, 2000, 105 (01) :133-165

[7]

DELEEUW K, 1959, J ANAL MATH, V7, P89, DOI DOI 10.1007/BF02787682

[8]

DeVore Ronald A., 1993, Constructive Approximation

[9] Strong estimates of the weighted simultaneous approximation by the Bernstein and Kantorovich operators and their iterated Boolean sums (vol 200, pg 92, 2015) [J].

Draganov, Borislav R. .

JOURNAL OF APPROXIMATION THEORY, 2020, 252

[10]

FELBECKER G, 1979, MANUSCRIPTA MATH, V29, P229, DOI 10.1007/BF01303629

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