Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type

In this paper, we introduce a family of [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaj...

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Detalles Bibliográficos
Autores principales: Cai, Qing-Bo, Zhou, Guorong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182413/
https://www.ncbi.nlm.nih.gov/pubmed/30363771
http://dx.doi.org/10.1186/s13660-018-1862-0
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author Cai, Qing-Bo
Zhou, Guorong
author_facet Cai, Qing-Bo
Zhou, Guorong
author_sort Cai, Qing-Bo
collection PubMed
description In this paper, we introduce a family of [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.
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spelling pubmed-61824132018-10-22 Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type Cai, Qing-Bo Zhou, Guorong J Inequal Appl Research In this paper, we introduce a family of [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence. Springer International Publishing 2018-10-01 2018 /pmc/articles/PMC6182413/ /pubmed/30363771 http://dx.doi.org/10.1186/s13660-018-1862-0 Text en © The Author(s) 2018 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
Zhou, Guorong
Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title_full Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title_fullStr Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title_full_unstemmed Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title_short Blending type approximation by [Formula: see text] operators of bivariate tensor product of λ-Bernstein–Kantorovich type
title_sort blending type approximation by [formula: see text] operators of bivariate tensor product of λ-bernstein–kantorovich type
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182413/
https://www.ncbi.nlm.nih.gov/pubmed/30363771
http://dx.doi.org/10.1186/s13660-018-1862-0
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