Kolmogorov and linear widths of classes of s-monotone integrable functions - Konovalov, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
Let s N and let Δ^s_+ be the set of functions x 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 I. For the classes Δ^s_+ B_p := Δ^s_+ 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 ≤ q < p ≤ ∞.