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.
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页数：34
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