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Date
2020-08-21
Author
Foupouagnigni, MamaWouodjié, Merlin Mouafo
Subject
510  Mathematics  Bernštejn-PolynomMultivariates PolynomGleichmäßige KonvergenzMonotonieKonvexität
URI
doi:10.17170/kobra-202008261652

doi:10.3390/math8091397
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Aufsatz

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 2227-7390
Sponsorship
Gefördert durch den Publikationsfonds der Universität Kassel
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Artikel  (Publikationen im Open Access gefördert durch die UB)
Citation
@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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3010 Wouodjié, Merlin Mouafo
4000 On Multivariate Bernstein Polynomials / Foupouagnigni, Mama
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5550 {{Bernštejn-Polynom}}
5550 {{Multivariates Polynom}}
5550 {{Gleichmäßige Konvergenz}}
5550 {{Monotonie}}
5550 {{Konvexität}}
7136 ##0##http://hdl.handle.net/123456789/11731

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2020-08-27T09:41:40Z
2020-08-21
doi:10.17170/kobra-202008261652
http://hdl.handle.net/123456789/11731
Gef&ouml;rdert durch den Publikationsfonds der Universit&auml;t 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&mdash;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
Wouodji&eacute;, Merlin Mouafo
doi:10.3390/math8091397
Bernštejn-Polynom
Multivariates Polynom
Gleichm&auml;&szlig;ige Konvergenz
Monotonie
Konvexit&auml;t
publishedVersion
EISSN 2227-7390
Issue 9
Mathematics
1397
Volume 8
false
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Namensnennung 4.0 International
Except where otherwise noted, this item's license is described as Namensnennung 4.0 International