Kolmogorov and linear widths of classes of s-monotone integrable functions

Abstract

Let $s \in \mathbb{N}$ and let $\Delta^s_+$ be the set of functions $x \mapsto \mathbb{R}$ on a finite interval $I$ such that the divided differences $[x; t_0, ... , t_s ]$ of order $s$ of these functions are nonnegative for all collections of $s + 1$ distinct points $t_0,..., t_s \in I$. For the classes $\Delta^s_+ B_p := \Delta^s_+ \bigcap B_p$ , where $B_p$ is the unit ball in $L_p$, we obtain orders of the Kolmogorov and linear widths in the spaces $L_q$ for $1 \leq q < p \leq \infty$.