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.

引用

页码：294 / 305

页数：11

共 16 条

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[6] Krylov N.V., Introduction to the Theory of Random Processes, (2002)
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[9] Pop O.T., Voronovskaja-type theorem for certain GBS operators, Glas. Mat. Ser III, 43, 63, (2008)
[10] Popoviciu T., Sur l’approximation des fonctions convexes d’ordre supérieur, Mathematica, 10, (1935)

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