A. Yu. Veretennikov, N. M. Mazutskiy, “On partial derivatives of Bernstein–Stancu polynomials for multivariate functions”, Mat. Sb., 2025, Volume 216, Number 7,Pages <nobr>3

On partial derivatives of Bernstein–Stancu polynomials for multivariate functions

A. Yu. Veretennikov^ab, N. M. Mazutskiy^c

^a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
^b Nikol'skii Mathematical Institute, Peoples' Friendship University of Russia, Moscow, Russia
^c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: The aim of the paper is to prove that mixed second-order derivatives of a function of several variables can be approximated in the $L_1$ norm by similar derivatives of modified Bernstein–Stancu polynomials in the case of the minimal possible smoothness.
Bibliography: 23 titles.

Keywords: modified Bernstein–Stancu polynomial, $L_1$-approximation of mixed derivatives.

MSC: 60F05; 41A10

Received: 04.07.2024 and 10.02.2025

DOI: 10.4213/sm10154