Ukrainian Mathematical Journal

, Volume 50, Issue 9, pp 1365–1375 | Cite as

On the approximation by Chebyshev splines in the metric of L p , p > 0

  • Yu. V. Kryakin


We prove a direct Jackson estimate for the approximation by Chebyshev splines in the classes L p , p > 0.


Polynomial Approximation Spline Function Divided Difference Main Lemma Spline Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Karlin, Total Positivity and Applications, Stanford University Press, Stanford (1968).Google Scholar
  2. 2.
    H. Johnen and K. Sherer, “Direct and inverse theorems for best approximations by A-splines,” in: K. Böhmer, G. Meinardus, and W. Schemp (editors), Spline Functions, Lect. Notes Math., 501 (1975), pp. 116–131.Google Scholar
  3. 3.
    L. L. Schumaker, Spline Functions: Basic Theory, Wiley, New York (1968).Google Scholar
  4. 4.
    Z. Wronich, “Moduli of smoothness associated with Chebyshev systems and approximation by L-splines,” in: Bl. Sendov, P. Petrushev, R. Maleev, and S. Tashev (editors), Constructive Theory of Functions’84, Sofia (1984), pp. 906–916.Google Scholar
  5. 5.
    Z. Wronich, Chebyshevian Splines, Jisse Math. CCCV, Warszawa (1990).Google Scholar
  6. 6.
    E. A. Storozhenko and P. Oswald, “Jackson theorem in the spaces Lp(Rk), 0 < p < 1,” Sib. Mat. Th., 4, 888–901 (1978).Google Scholar
  7. 7.
    P. Oswald, “Approximation by splines in the metric of Lp, 0 < p < 1,” Math. Nachr., 94, 69–96 (1980).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    E. A. Storozhenko and Yu. V. Kryakin, On the Whitney theorem in Lp-metric,” Mat. Sb., 186, No. 3, 131–142 (1995).MathSciNetGoogle Scholar
  9. 9.
    Yu. V. Kryakin, Approximation of Functions on a Unit Circle in the Spaces L p and H p [in Russian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Odessa (1985).Google Scholar
  10. 10.
    T. Popoviciu, “Sur la reste dans certaines formulas lineaires d’approximation de l’analyse,” Math. Cluj., 1 (24), 95–142 (1959).MathSciNetGoogle Scholar
  11. 11.
    H. Whitney, “On functions with bounded nth differences,” J. Math. Pure Appl., 36, 67–95 (1955).MathSciNetGoogle Scholar
  12. 12.
    V. Kh. Sendov and V. A. Popov, “On classes characterized by the best approximation by spline functions,” Mat. Zametki, 8, No. 2, 137–148 (1970).MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • Yu. V. Kryakin
    • 1
  1. 1.Odessa UniversityOdessa

Personalised recommendations