On the best non-symmetric L1-approximations by splines under constraints for their derivatives
Abstract
We find exact values of non-symmetric L1-approximations of classes Wr1 of periodic functions by splines s∈S2n,r−1 and s∈S2n,r (S2n,r is the set of 2π-periodic polynomial splines of degree r, of defect 1, with knots in the points kπ/n, k∈Z) such that 2π⋁0s(r−1)⩽ and \| s^{(r)} \| \leqslant 1 respectively when r is even, and, as a corollary, we obtain exact values for the corresponding best one-side approximations.
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DOI: https://doi.org/10.15421/249802
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Copyright (c) 1998 V.F. Babenko, I.N. Litviniuk, N.V. Parfinovych

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