Some approximation properties of (p, q)-Bernstein operators

被引：0

作者：

Kang, Shin Min ^{[1
,2
]}

Rafiq, Arif ^{[3
]}

Acu, Ana-Maria ^{[4
]}

Ali, Faisal ^{[5
]}

Kwun, Young Chel ^{[6
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 52828, South Korea

[2] Gyeongsang Natl Univ, RINS, Jinju 52828, South Korea

[3] Virtual Univ Pakistan, Dept Math & Stat, Lahore 54000, Pakistan

[4] Lucian Blaga Univ Sibiu, Dept Math & Informat, Str Dr I Ratiu 5-7, Sibiu 550012, Romania

[5] Bahauddin Zakariya Univ, Ctr Adv Studies Pure & Appl Math, Multan 60800, Pakistan

[6] Dong A Univ, Dept Math, Busan 49315, South Korea

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2016年

关键词：

(p; q)-Bernstein operators; q)-calculus; Voronovskaja type theorem; K-functional; Ditzian-Totik first order modulus of smoothness;

D O I：

10.1186/s13660-016-1111-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the (p, q)-analog of Bernstein operators. It is proved that, when the function is convex, the (p, q)-Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.

引用

页数：10

共 19 条

[1] (p,q)-Generalization of Szasz-Mirakyan operators [J].

Acar, Tuncer .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (10) :2685-2695

[2] On Pointwise Convergence of q-Bernstein Operators and Their q-Derivatives [J].

Acar, Tuncer ;

Aral, Ali .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2015, 36 (03) :287-304

[3] Approximation Properties of Bivariate Extension of q-Bernstein-Schurer-Kantorovich operators [J].

Acu, Ana Maria ;

Muraru, Carmen Violeta .

RESULTS IN MATHEMATICS, 2015, 67 (3-4) :265-279

[4] Stancu-Schurer-Kantorovich operators based on q-integers [J].

Acu, Ana Maria .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 259 :896-907

[5] On a q-analogue of Stancu operators [J].

Agratini, Octavian .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (01) :191-198

[6]

[Anonymous], 1987, Seminar on numerical and statistical calculus

[7]

[Anonymous], 1995, J. Nonlinear Math. Phys.

[8]

Aral A., 2013, Applications of q-Calculus in Operator Theory

[9] Bernstein-type operators which preserve polynomials [J].

Cardenas-Morales, D. ;

Garrancho, P. ;

Rasa, I. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (01) :158-163

[10]

Ditzian Z., 1987, Springer Series in Computational Mathematics

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