On Multivariate Bernstein Polynomials

被引：7

作者：

Foupouagnigni, Mama ^{[1
,2
]}

Mouafo Wouodjie, Merlin ^{[3
]}

机构：

[1] African Inst Math Sci, POB 608, Limbe, Cameroon

[2] Univ Yaounde I, Higher Teacher Training Coll, POB 47, Yaounde, Cameroon

[3] Univ Kassel, Inst Math, Heinrich Plett Str 40, D-34132 Kassel, Germany

来源：

MATHEMATICS | 2020年 / 8卷 / 09期

关键词：

Bernstein polynomials; functions of several variables; derivatives; uniform convergence; order of convergence; monotonicity; convexity; upper and lower bounds; APPROXIMATION; COMBINATIONS;

D O I：

10.3390/math8091397

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 thep-th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions.

引用

页数：34