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

• Дата: 2022
• Автори: Babich, Yu. P., Mikhailova, T. F., Бабич, Ю. П., Михайлова, Т. Ф.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2022
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/7124
• Назва журналу: 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...