On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines

We obtain the exact asymptotics (as n ) of the best L₁-approximations of classes of periodic functions by splines s S_{2n, r – 1} and s S_{2n, r + k – 1} (S_{2n, r} is the set of 2-periodic polynomial splines of order r and defect 1 with nodes at the points k/n, k Z) under certain restrictions on their derivatives.