Convergence of λ-Bernstein operators based on (p, q)-integers

被引：13

作者：

Cai, Qing-Bo ^{[1
]}

Cheng, Wen-Tao ^{[2
]}

机构：

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

[2] Anqing Normal Univ, Sch Math & Computat Sci, Anqing, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2020年 / 2020卷 / 01期

基金：

中国国家自然科学基金;

关键词：

lambda-Bernstein operators; (p; q)-integers; Moduli of continuity; Rate of convergence; Lipschitz continuous functions; APPROXIMATION PROPERTIES; STATISTICAL APPROXIMATION; Q)-ANALOG;

D O I：

10.1186/s13660-020-2309-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we construct a new class of positive linear lambda-Bernstein operators based on (p, q)-integers. We obtain a Korovkin type approximation theorem, study the rate of convergence of these operators by using the conception of K-functional and moduli of continuity, and also give a convergence theorem for the Lipschitz continuous functions.

引用

页数：17

共 29 条

[1] On a Modification of (p, q)-Szasz-Mirakyan Operators [J].

Acar, Tuncer ;

Agrawal, Purshottam Narain ;

Kumar, A. Sathish .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2018, 12 (01) :155-167

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

Acar, Tuncer .

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

[3] Approximation properties of λ-Kantorovich operators [J].

Acu, Ana-Maria ;

Manav, Nesibe ;

Sofonea, Daniel Florin .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,

[4]

Al-Abied A.A.H., 2020, AZERB J MATH, V10

[5] On Some Statistical Approximation by (p, q)-Bleimann, Butzer and Hahn Operators [J].

Ansari, Khursheed J. ;

Ahmad, Ishfaq ;

Mursaleen, M. ;

Hussain, Iqtadar .

SYMMETRY-BASEL, 2018, 10 (12)

[6]

Cai Q.B., 2017, J INEQUAL APPL, V2017

[7]

Cai Q.B., 2018, J INEQUAL APPL, V2018

[8] Statistical approximation properties of λ-Bernstein operators based on q-integers [J].

Cai, Qing-Bo ;

Zhou, Guorong ;

Li, Junjie .

OPEN MATHEMATICS, 2019, 17 :487-498

[9] On (p, q)-analogue of Kantorovich type Bernstein-Stancu-Schurer operators [J].

Cai, Qing-Bo ;

Zhou, Guorong .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 276 :12-20

[10]

Cheng WT, 2019, J INEQUAL APPL, DOI 10.1186/s13660-019-2053-3

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