No Jackson-type estimates for piecewise $q$-monotone, $q\ge3$, trigonometric approximation

• Date: 2022
• Main Authors: Leviatan , D., Motorna, O. V., Shevchuk, I. A., Шевчук, Ігор
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7081
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We say that a function $f \in C[a,b]$ is $q$-monotone, $q \ge 3$, if $f\in C^{q-2}(a,b)$ and $f^{(q-2)}$ is convex in $(a,b)$. Let $f$ be continuous and $2\pi$-periodic, and change its $q$-monotonicity finitely many times in $[-\pi,\pi]$. We are interested in estimating the degree of appro...