No Jackson-type estimates for piecewise $q$-monotone, $q\ge 3$, trigonometric approximation

Dany Leviatan, Oksana V. Motorna, Igor A. Shevchuk

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…