Sharp inequalities of Kolmogorov type for non-periodic functions on the real domain

T.R. Bіkkuzhyna (Oles Honchar Dnipropetrovsk National University)
V.A. Kofanov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0003-0392-2257

Abstract


We obtained sharp inequalities of Kolmogorov type for non-periodic functions on the real domain. The obtained results were applied to solve some extremum problems for non-periodic functions and splines on the real domain.

Keywords


inequality of Kolmogorov type; norm; local norm; problem of Bojanov–Naidenov type; nonperiodic splines

References


Kofanov V.A. "Inequalities of Kolmogorov and Bernstein type", Pratsі Ukrajins'kogo matematychnogo kongresu (Approximation theory and Fourier analysis), 2001, Kyiv, 2002; pp. 84-99. (in Russian)

Kofanov V.A. "Sharp inequalities of Bernstein and Kolmogorov type", East J. Approx, 2005; 11(2): pp. 131-145.

Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", J. d'Analyse Mathematique, 1999; 78: pp. 263-280.

Kofanov V.A. "Some extremum problems in different metrics for differentiable functions on the real domain", Ukrainian Math. J., 2009; 61(6): pp. 765-776. (in Russian)

Erdös P. "Open problems", Open Problems in Approximation Theory (B. Bojanov, ed.), SCT Publishing, Singapur, 1994; pp. 238-242.

Magaril-Il'yaev G.G. "Best approximations of functional classes by splines on the real domain", Trudy mat. in-ta im. Steklova, 1992; pp. 153-154. (in Russian)

Kofanov V.A. "Inequalities for non-periodic splines and their derivatives on the real domain", Ukrainian Math. J., 2014; 66(2): pp. 216-225. (in Russian)




DOI: https://dx.doi.org/10.15421/241501

  

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Copyright (c) 2015 T.R. Bіkkuzhyna, V.A. Kofanov

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