Nonsymmetric approximations of classes of periodic functions by splines of defect 2 and Jackson-type inequalities

Abstract

We determine the exact values of the best (α, β)-approximations and the best one-sided approximations of classes of differentiable periodic functions by splines of defect 2. We obtain new sharp Jackson-type inequalities for the best approximations and the best one-sided approximations by splines of defect 2.