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Approximation of sine-shaped functions by constants in the spaces L p , < 1

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We investigate the best approximations of sine-shaped functions by constants in the spaces L p for p < 1. In particular, we find the best approximation of perfect Euler splines by constants in the spaces L p for certain p∈(0,1).

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REFERENCES

  1. G. H. Hardy J. E. Littlewood G. Pólya (1948) Inequalities Izd. Inostr. Lit. Moscow

    Google Scholar 

  2. V. M. Tikhomirov G. G. Magaril-Il’yaev (1985) Inequalities for derivatives A. N. Kolmogorov (Eds) Selected Works. Mathematics and Mechanics Nauka Moscow 387–390

    Google Scholar 

  3. V. V. Arestov V. N. Gabushin (1995) ArticleTitleBest approximation of unbounded operators by bounded operators Izv. Vyssh. Uchebn. Zaved., Ser. Mat. 11 44–66

    Google Scholar 

  4. V. V. Arestov (1996) ArticleTitleApproximation of unbounded operators by bounded operators and related extremal problems Usp. Mat. Nauk 51 IssueID6 88–124

    Google Scholar 

  5. V. F. Babenko V. A. Kofanov S. A. Pichugov (1998) ArticleTitleInequalities of Kolmogorov type and some their applications in approximation theory Rend. Circ. Mat. Palermo, Ser. II, Suppl. 52 223–237

    Google Scholar 

  6. V. F. Babenko V. A. Kofanov S. A. Pichugov (1999) On the exact inequalities of Kolmogorov type and some of their applications New Approaches in Nonlinear Analysis Hadronic Press Palm Harbor 9–50

    Google Scholar 

  7. V. F. Babenko (2000) ArticleTitleInvestigations of Dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications Ukr. Mat. Zh. 52 IssueID1 9–29

    Google Scholar 

  8. V. F. Babenko V. A. Kofanov S. A. Pichugov (2002) Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions B. D. Bojanov (Eds) Approximation Theory: A Volume Dedicated to Blagovest Sendov 2002 Darba Sofia 24–53

    Google Scholar 

  9. V. N. Gabushin, “Some inequalities for derivatives of functions,” in: Methods of Regularization of Unstable Problems [in Russian], Ural Scientific Center, Academy of Sciences of the USSR (1976), pp. 20–26.

  10. V. F. Babenko V. A. Kofanov S. A. Pichugov (2001) ArticleTitleExact Kolmogorov-type inequalities with bounded leading derivative in the case of low smoothness Ukr. Mat. Zh. 53 IssueID10 1298–1308

    Google Scholar 

  11. S. A. Pichugov (1995) ArticleTitleApproximation of the contractions of periodic functions in the spaces L p, p < 1 Ukr. Mat. Zh. 47 IssueID12 1708–1711

    Google Scholar 

  12. N. P. Korneichuk (1976) Extremal Problems in Approximation Theory Naukova Dumka Kiev

    Google Scholar 

  13. V. V. Arestov (1982) ArticleTitleOn integral inequalities for trigonometric polynomials and their derivatives Izv. Akad. Nauk SSSR, Ser. Mat. 45 IssueID1 3–32

    Google Scholar 

  14. N. P. Korneichuk (1987) Exact Constants in Approximation Theory Nauka Moscow

    Google Scholar 

  15. N. P. Korneichuk V. F. Babenko A. A. Ligun (1992) Extremal Properties of Polynomials and Splines Naukova Dumka Kiev

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. F. Babenko

  2. Dnepropetrovsk National University, Dnepropetrovsk

    V. A. Kofanov

  3. Dnepropetrovsk Agricultural University, Dnepropetrovsk

    S. A. Pichugov

Authors
  1. V. F. Babenko
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  2. V. A. Kofanov
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  3. S. A. Pichugov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 745–762, June, 2004.

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Babenko, V.F., Kofanov, V.A. & Pichugov, S.A. Approximation of sine-shaped functions by constants in the spaces L p , < 1. Ukr Math J 56, 882–903 (2004). https://doi.org/10.1007/PL00022172

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  • DOI: https://doi.org/10.1007/PL00022172

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