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2020-08-21Subject
510 Mathematics Bernštejn-PolynomMultivariates PolynomGleichmäßige KonvergenzMonotonieKonvexitätMetadata
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Aufsatz![](/themes/Mirage2/images/Open_Access_logo_PLoS_transparent.svg)
On Multivariate Bernstein Polynomials
Abstract
In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of the derivatives, order of convergence, monotonicity, fixed sign for the p-th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions.
Citation
In: Mathematics Volume 8 / Issue 9 (2020-08-21) , S. 1397 ; EISSN 2227-7390Sponsorship
Gefördert durch den Publikationsfonds der Universität KasselCitation
@article{doi:10.17170/kobra-202008261652,
author={Foupouagnigni, Mama and Wouodjié, Merlin Mouafo},
title={On Multivariate Bernstein Polynomials},
journal={Mathematics},
year={2020}
}
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2020-08-27T09:41:40Z 2020-08-27T09:41:40Z 2020-08-21 doi:10.17170/kobra-202008261652 http://hdl.handle.net/123456789/11731 Gefördert durch den Publikationsfonds der Universität Kassel eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Bernstein polynomials functions of serveral variables derivatives uniform convergence order of convergence monotonicity convexity upper and lower bounds 510 On Multivariate Bernstein Polynomials Aufsatz In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of the derivatives, order of convergence, monotonicity, fixed sign for the p-th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions. open access Foupouagnigni, Mama Wouodjié, Merlin Mouafo doi:10.3390/math8091397 Bernštejn-Polynom Multivariates Polynom Gleichmäßige Konvergenz Monotonie Konvexität publishedVersion EISSN 2227-7390 Issue 9 Mathematics 1397 Volume 8 false
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