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On the best non-symmetric L1-approximations by splines under constraints for their derivatives

V.F. Babenko (Dnipropetrovsk State University), https://orcid.org/0000-0001-6677-1914
I.N. Litviniuk (Dnipropetrovsk State University)
N.V. Parfinovych (Dnipropetrovsk State University), https://orcid.org/0000-0002-3448-3798

Abstract


We find exact values of non-symmetric L1-approximations of classes Wr1 of periodic functions by splines sS2n,r1 and sS2n,r (S2n,r is the set of 2π-periodic polynomial splines of degree r, of defect 1, with knots in the points kπ/n, kZ) such that 2π0s(r1) 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.

References


Babenko V.F. "The best L_1-approximations of W^r_1 classes by splines from W^r_1", Ukrainian Math. J., 1994; 46(10): pp. 1410-1413. (in Russian) doi:10.1007/BF01066101

Babenko V.F. "Mean approximations under constraints for derivatives of approximating functions", Vopr. analiza i priblizh., 1989; pp. 9-18. (in Russian)

Korneichuk N.P. Splines in approximation theory, Nauka, 1984. (in Russian)

Korneichuk N.P. Exact constants in approximation theory, Nauka, 1987. (in Russian)

Korneichuk N.P. Extremum problems in approximation theory, 1976. (in Russian)




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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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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