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Article

On partial derivatives of multivariate Bernstein polynomials

Siberian Advances in Mathematics. 2016. Vol. 26. No. 4. P. 231-242.
Veretennikov A., Veretennikova E.

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.