On partial derivatives of multivariate Bernstein polynomials

被引：0
|
作者：
Veretennikov A.Y. [1 ,2 ,3 ]
Veretennikova E.V. [4 ]
机构：
[1] University of Leeds, Leeds
[2] Higher School of Economics, Moscow
[3] Institute for Information Transmission Problems, Moscow
[4] Moscow State Pedagogical University, Moscow
来源：
Siberian Advances in Mathematics | 2016年 / 26卷 / 4期
关键词：
convergence; multivariate Bernstein polynomial; partial derivative;
D O I：
10.3103/S1055134416040039
中图分类号：
学科分类号：
摘要：
It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus. © 2016, Allerton Press, Inc.
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页码：294 / 305
页数：11
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