Approximation properties of λ-Kantorovich operators

In the present paper, we study a new type of Bernstein operators depending on the parameter [Formula: see text] . The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness...

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Detalles Bibliográficos
Autores principales: Acu, Ana-Maria, Manav, Nesibe, Sofonea, Daniel Florin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096926/
https://www.ncbi.nlm.nih.gov/pubmed/30839580
http://dx.doi.org/10.1186/s13660-018-1795-7
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author Acu, Ana-Maria
Manav, Nesibe
Sofonea, Daniel Florin
author_facet Acu, Ana-Maria
Manav, Nesibe
Sofonea, Daniel Florin
author_sort Acu, Ana-Maria
collection PubMed
description In the present paper, we study a new type of Bernstein operators depending on the parameter [Formula: see text] . The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.
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spelling pubmed-60969262018-08-24 Approximation properties of λ-Kantorovich operators Acu, Ana-Maria Manav, Nesibe Sofonea, Daniel Florin J Inequal Appl Research In the present paper, we study a new type of Bernstein operators depending on the parameter [Formula: see text] . The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given. Springer International Publishing 2018-08-02 2018 /pmc/articles/PMC6096926/ /pubmed/30839580 http://dx.doi.org/10.1186/s13660-018-1795-7 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
Acu, Ana-Maria
Manav, Nesibe
Sofonea, Daniel Florin
Approximation properties of λ-Kantorovich operators
title Approximation properties of λ-Kantorovich operators
title_full Approximation properties of λ-Kantorovich operators
title_fullStr Approximation properties of λ-Kantorovich operators
title_full_unstemmed Approximation properties of λ-Kantorovich operators
title_short Approximation properties of λ-Kantorovich operators
title_sort approximation properties of λ-kantorovich operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096926/
https://www.ncbi.nlm.nih.gov/pubmed/30839580
http://dx.doi.org/10.1186/s13660-018-1795-7
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