Approximation properties of λ-Bernstein operators

In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text] , we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymp...

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Detalles Bibliográficos
Autores principales: Cai, Qing-Bo, Lian, Bo-Yong, 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/PMC5856904/
https://www.ncbi.nlm.nih.gov/pubmed/29576718
http://dx.doi.org/10.1186/s13660-018-1653-7
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author Cai, Qing-Bo
Lian, Bo-Yong
Zhou, Guorong
author_facet Cai, Qing-Bo
Lian, Bo-Yong
Zhou, Guorong
author_sort Cai, Qing-Bo
collection PubMed
description In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text] , we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text] , and we see that in some cases the errors are smaller than [Formula: see text] to f.
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spelling pubmed-58569042018-03-21 Approximation properties of λ-Bernstein operators Cai, Qing-Bo Lian, Bo-Yong Zhou, Guorong J Inequal Appl Research In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text] , we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text] , and we see that in some cases the errors are smaller than [Formula: see text] to f. Springer International Publishing 2018-03-16 2018 /pmc/articles/PMC5856904/ /pubmed/29576718 http://dx.doi.org/10.1186/s13660-018-1653-7 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
Lian, Bo-Yong
Zhou, Guorong
Approximation properties of λ-Bernstein operators
title Approximation properties of λ-Bernstein operators
title_full Approximation properties of λ-Bernstein operators
title_fullStr Approximation properties of λ-Bernstein operators
title_full_unstemmed Approximation properties of λ-Bernstein operators
title_short Approximation properties of λ-Bernstein operators
title_sort approximation properties of λ-bernstein operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5856904/
https://www.ncbi.nlm.nih.gov/pubmed/29576718
http://dx.doi.org/10.1186/s13660-018-1653-7
work_keys_str_mv AT caiqingbo approximationpropertiesoflbernsteinoperators
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AT zhouguorong approximationpropertiesoflbernsteinoperators

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