On Multivariate Bernstein Polynomials

Mama Foupouagnigni and Merlin Mouafo Wouodjié
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Mama Foupouagnigni: African Institute for Mathematical Sciences, P.O. Box 608, Limbe, Cameroon
Merlin Mouafo Wouodjié: Institute of Mathematics, University of Kassel, Heinrich-Plett Str. 40, 34132 Kassel, Germany

Mathematics, 2020, vol. 8, issue 9, 1-34

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.

Keywords: Bernstein polynomials; functions of several variables; derivatives; uniform convergence; order of convergence; monotonicity; convexity; upper and lower bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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