On the best L1-approximations of functional classes by splines under restrictions imposed on their derivatives

  • V. F. Babenko
  • N. V. Parfinovych Днепропетр. нац. ун-т

Abstract

We find the exact asymptotics (n) of the best L1-approximations of classes Wr1 of periodic functions by splines sS2n,r1 (S2n,r1 is a set of 2π-periodic polynomial splines of order r1, defect one, and with nodes at the points kπ/n,k) such that V2π0s(r1)1+ɛn, where {ɛn}n=1 is a decreasing sequence of positive numbers such that ɛnn2 and ɛn0 as n.
Published
25.04.1999
How to Cite
Babenko, V. F., and N. V. Parfinovych. “On the Best L1-Approximations of Functional Classes by Splines under Restrictions Imposed on Their Derivatives”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 4, Apr. 1999, pp. 435-44, https://umj.imath.kiev.ua/index.php/umj/article/view/4629.
Section
Short communications