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

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

Abstract In the present paper, we construct a new class of positive linear λ-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...

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Main Authors: Qing-Bo Cai, Wen-Tao Cheng
Format: Article
Language:English
Published: SpringerOpen 2020-02-01
Series:Journal of Inequalities and Applications
Subjects:
λ-Bernstein operators
(p, q)-integers
Moduli of continuity
Rate of convergence
Lipschitz continuous functions
Online Access:https://doi.org/10.1186/s13660-020-2309-y
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spelling doaj-d408133a5aa647f2972840175030356c2021-02-14T12:03:33ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-02-012020111710.1186/s13660-020-2309-yConvergence of λ-Bernstein operators based on (p, q)-integersQing-Bo Cai0Wen-Tao Cheng1School of Mathematics and Computer Science, Quanzhou Normal UniversitySchool of Mathematics and Computation Science, Anqing Normal UniversityAbstract In the present paper, we construct a new class of positive linear λ-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.https://doi.org/10.1186/s13660-020-2309-yλ-Bernstein operators(p, q)-integersModuli of continuityRate of convergenceLipschitz continuous functions
collection DOAJ
language English
format Article
sources DOAJ
author Qing-Bo Cai
Wen-Tao Cheng
spellingShingle Qing-Bo Cai
Wen-Tao Cheng
Convergence of λ-Bernstein operators based on (p, q)-integers
Journal of Inequalities and Applications
λ-Bernstein operators
(p, q)-integers
Moduli of continuity
Rate of convergence
Lipschitz continuous functions
author_facet Qing-Bo Cai
Wen-Tao Cheng
author_sort Qing-Bo Cai
title Convergence of λ-Bernstein operators based on (p, q)-integers
title_short Convergence of λ-Bernstein operators based on (p, q)-integers
title_full Convergence of λ-Bernstein operators based on (p, q)-integers
title_fullStr Convergence of λ-Bernstein operators based on (p, q)-integers
title_full_unstemmed Convergence of λ-Bernstein operators based on (p, q)-integers
title_sort convergence of λ-bernstein operators based on (p, q)-integers
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1029-242X
publishDate 2020-02-01
description Abstract In the present paper, we construct a new class of positive linear λ-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.
topic λ-Bernstein operators
(p, q)-integers
Moduli of continuity
Rate of convergence
Lipschitz continuous functions
url https://doi.org/10.1186/s13660-020-2309-y
work_keys_str_mv AT qingbocai convergenceoflbernsteinoperatorsbasedonpqintegers
AT wentaocheng convergenceoflbernsteinoperatorsbasedonpqintegers
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