On one property of the modulus of continuity for periodic functions of higher orders

• Date: 2022
• Main Authors: Maksymenkova , Yu. A., Michaylova , Т. F., Максименкова, Ю. А., 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/7217
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For the moduli of continuity of $2\pi$-periodic functions $\omega_k(f,h)$ of order $k = 1,2,\ldots, $ we prove the inequalities$$\omega_k(f,\pi)\leq\frac{2^k}{C_k^{[\frac{k}{2}]}}\frac{1}{\pi}\int\limits_0^{\pi}\omega_k(f,h)dh,$$for even $k.$ The inequalities are exact in the spaces $C_{2\...