On partial derivatives of Bernstein–Stancu polynomials for multivariate functions

The aim of the paper is to prove that mixed second-order derivatives of a function of several variables can be approximated in the L1 norm by similar derivatives of modified Bernstein–Stancu polynomials in the case of the minimal possible smoothness. Bibliography: 23 titles. © 2025 Russian Academy of Sciences, Steklov Mathematical Institute of RAS.

Авторы
Veretennikov Alexander Yu 1, 2 , Mazutskiy Nikolay M. 3
Журнал
Sbornik Mathematics
Издательство
Russian Academy of Sciences
Номер выпуска
7
Язык
Английский
Страницы
877-901
Статус
Опубликовано
Ссылка
Внешняя ссылка
DOI
10.4213/SM10154E
Том
216
Год
2025
Организации
  • 1 Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Moscow Oblast, Russian Federation
  • 2 Nikol’skii Mathematical Institute, RUDN University, Moscow, Moscow Oblast, Russian Federation
  • 3 Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Moscow Oblast, Russian Federation
Ключевые слова
L1-approximation of mixed derivatives; modified Bernstein–Stancu polynomial
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