A remark concerning the modulus of smoothness introduced by Ditzian and Totik

• Date: 1995
• Main Authors: Dyuzhenkova, O. Yu., Дюженкова, О. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5556
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For each functionf(x) continuous on the segment [−1, 1], we set \(\tilde f(t) = f(\cos t)\) . We study the relationship between the ordinarykth modulus of continuity \(\omega _k (\tau ,\tilde f^{(r)} )\) of therth derivative \(\tilde f^{(r)}\) of the function \(\tilde f\) and thekth modul...