On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives

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


We find the exact asymptotics ($n → ∞$) of the best $L_1$-approximations of classes $W_1^r$ of periodic functions by splines $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ is a set of $2π$-periodic polynomial splines of order $r−1$, defect one, and with nodes at the points $kπ/n,\; k ∈ ℤ$) such that $V_0^{2π} s^{( r-1)} ≤ 1+ɛ_n$, where $\{ɛ_n\}_{n=1}^{ ∞}$ is a decreasing sequence of positive numbers such that $ɛ_n n^2 → ∞$ and $ɛ_n → 0$ as $n → ∞$.
How to Cite
Babenko, V. F., and N. V. Parfinovych. “On the Best $L_1$-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.
Short communications