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Ukrainian Mathematical Journal

, Volume 49, Issue 7, pp 1067–1074 | Cite as

Approximation of certain classes of differentiable functions by generalized splines

  • O. V. Polyakov
Article

Abstract

We find the exnet value of the best (α, β)-approximation by generalized Chebyshev splines for a class of functions differentiable with weight on [−1, 1].

Keywords

Differentiable Function Contemporary Problem Chebyshev Polynomial Duality Theorem Space 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.

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References

  1. 1.
    V. F. Babenko, “Asymmetric approximations in spaces of summable functions.” Ukr. Mat. Zh., 34, No. 4, 409–416 (1982).MathSciNetGoogle Scholar
  2. 2.
    N. P. Korneichuk, Exact Constants in the Theory of Approximations [in Russian], Nauka, Moscow, (1987).Google Scholar
  3. 3.
    S. Karlin and W. J. Studden, Tchebycheff Systems: with Applications in Analysis and Statistics [Russian translation], Nauka, Moscow (1976).Google Scholar
  4. 4.
    S. Karlin and L. Schumaker, “The fundamental theorem of algebra for Tchebysheffian monosplines,” J. Analyse Math., 5, No. 20, 233–270 (1967).CrossRefMathSciNetGoogle Scholar
  5. 5.
    L. Schumaker, “Uniform approximation by Tchebysheffian spline functions,” J. Math. Mech., 18, No. 4, 369–378 (1968).zbMATHMathSciNetGoogle Scholar
  6. 6.
    A. A. Zhensykbaev, “Chebyshev splines and their properties,” in: Proceedings of the International Conference “Theory of Approximation of Functions” [in Russian], Nauka, Moscow (1987), pp. 164–168.Google Scholar
  7. 7.
    V. F. Babenko and O. V. Polyakov, “On asymmetric approximations of classes of differentiable functions by splines in the space L 1 [−1, 1],”, in: Optimization of Methods for Approximation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 27–34.Google Scholar
  8. 8.
    O. Ya. Shevaldina, “On the approximation of classes W pr by polynomial splines in the mean,” in: Approximation in Special and Abstract Banach Spaces [in Russian], Ural Scientific Center Academy of Sciences of the USSR, Sverdlovsk (1987), pp. 113–120.Google Scholar
  9. 9.
    V. F. Babenko, “On the existence of perfect splines and monosplines with given zeros,” in: Studies of Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk. (1987), pp. 6–9.Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • O. V. Polyakov

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