On the best L_1-approximations of functional classes by splines under restrictions imposed on their derivatives - Babenko, V. F.; Parfinovych, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
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 → ∞.