Fine-grained evaluations of the best estimates for smooth functions in $C_{2\pi}$ in terms of linear combinations of modules of continuity of their derivatives

• Date: 2022
• Main Authors: Babich, Yu. P., Mikhailova, T. F., Бабич, Ю. П., Михайлова, Т. Ф.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7124
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For the best approximations of $e_{n-1}(f)$ functions in $C^1_{2\pi}$ by trigonometric polynomials, Zhuk proved the exact Jackson inequality $e_{n-1}(f)\leqslant \dfrac{\pi}{4n}\omega\left(f',\dfrac{\pi}{n}\right)$. In this paper, we prove the following version of Jackson&#039...