On one problem for comonotone approximation

• Datum: 2005
• Hauptverfasser: Nesterenko, A. N., Petrova, T. O., Нестеренко, А. Н., Петрова, Т. О.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2005
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3697
• Назва журналу: 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.