Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text] -integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of...

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Detalles Bibliográficos
Autores principales: Cai, Qing-Bo, Xu, Xiao-Wei, Zhou, Guorong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5686288/
https://www.ncbi.nlm.nih.gov/pubmed/29213195
http://dx.doi.org/10.1186/s13660-017-1559-9
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author Cai, Qing-Bo
Xu, Xiao-Wei
Zhou, Guorong
author_facet Cai, Qing-Bo
Xu, Xiao-Wei
Zhou, Guorong
author_sort Cai, Qing-Bo
collection PubMed
description In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text] -integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.
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spelling pubmed-56862882017-12-04 Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators Cai, Qing-Bo Xu, Xiao-Wei Zhou, Guorong J Inequal Appl Research In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text] -integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions. Springer International Publishing 2017-11-14 2017 /pmc/articles/PMC5686288/ /pubmed/29213195 http://dx.doi.org/10.1186/s13660-017-1559-9 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Cai, Qing-Bo
Xu, Xiao-Wei
Zhou, Guorong
Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title_full Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title_fullStr Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title_full_unstemmed Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title_short Bivariate tensor product [Formula: see text] -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators
title_sort bivariate tensor product [formula: see text] -analogue of kantorovich-type bernstein-stancu-schurer operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5686288/
https://www.ncbi.nlm.nih.gov/pubmed/29213195
http://dx.doi.org/10.1186/s13660-017-1559-9
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