Shape-Preserving Widths of Weighted Sobolev-Type Classes of Positive, Monotone, and Convex Functions on a Finite Interval

Abstract

Abstract. Let I be a finite interval, r∈N and ρ(t)= dist {t, I} , t∈ I . Denote by Δ s + L q the subset of all functions y∈ L q such that the s -difference Δ s τ y(t) is nonnegative on I , $$\forall$$ τ>0 . Further, denote by $$\Delta^s_+W^r_{p,\alpha}$$ , 0≤α 0 . For s=0,1,2 , we obtain two-sided estimates of the shape-preserving widths