On one problem for comonotone approximation

• Date: 2005
• Main Authors: Nesterenko, A. N., Petrova, T. O., Нестеренко, А. Н., Петрова, Т. О.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3697
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For a comonotone approximation, we prove that an analog of the second Jackson inequality with generalized Ditzian - Totik modulus of smoothness $\omega^{\varphi}_{k, r}$ is invalid for $(k, r) = (2, 2)$ even if the constant depends on a function.