On the best relative nonsymmetric approximations of classes of periodic functions by splines

Ye.N. Karpova (Oles Honchar Dnipropetrovsk National University)
N.V. Parfinovich (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-3448-3798

Abstract


We find exact asymptotic equalities for the best nonsymmetric approximations of classes $$$W_1^r$$$ by splines with bounded higher derivative.

References


Babenko V.F. "On the best $$$L_1$$$-approximations by splines under the constraints on their derivatives", Matem. zametki, 1992; 51(5): pp. 12-19. (in Russian) doi:10.1007/BF01262172

Babenko V.F., Parfinovich N.V. "On the best $$$L_1$$$-approximation of functional classes by splines with constraints for their derivatives", Ukrainian Math. J., 1999; 51(4): pp. 435-444. (in Russian) doi:10.1007/BF02591753

Gubanova V.V., Parfinovich N.V. "On exact values of the best relative nonsymmetric approximations of classes of periodic functions by splines", Res. Math., 2006; 14: pp. 21-28. (in Russian)

Korneichuk N.P. Exact constants in approximation theory, Nauka, Moscow, 1987; 424 p. (in Russian)

Parfinovich N.V. "On exact asymptotics of the best relative approximations of classes of periodic functions by splines", Ukrainian Math. J., 2001; 53(4): pp. 489-500. (in Russian) doi:10.1023/A:1012322504060




DOI: https://doi.org/10.15421/240811

  

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Copyright (c) 2008 Ye.N. Karpova, N.V. Parfinovich

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