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On Multivariate Bernstein Polynomials

Foupouagnigni, Mama
Wouodjié, Merlin Mouafo

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.

Sponsor
Gefördert durch den Publikationsfonds der Universität Kassel
Citation
In: Mathematics Volume 8 / Issue 9 (2020-08-21) , S. 1397; EISSN 2227-7390
Collections
@article{doi:10.17170/kobra-202008261652,
  author    ={Foupouagnigni, Mama and Wouodjié, Merlin Mouafo},
  title    ={On Multivariate Bernstein Polynomials},
  keywords ={510 and Bernštejn-Polynom and Multivariates Polynom and Gleichmäßige Konvergenz and Monotonie and Konvexität},
  copyright  ={http://creativecommons.org/licenses/by/4.0/},
  language ={en},
  journal  ={Mathematics},
  year   ={2020-08-21}
}