Skip to main content
SpringerLink
Log in

On the uniqueness of elements of the best approximation and the best one-sided approximation in the spaceL 1

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

The problem of the uniqueness of elements of the best approximations in the spaceL 1 [a, b] is studied. We consider the problem of the best approximation and the best (α, β)-approximation of continuous functions and the problem of the best one-sided approximation of continuously differentiable functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. F. Babenko, “Nonsymmetric approximations in the spaces of summable functions,”Ukr. Mat. Zh.,34, No. 4, 409–416 (1982).

    Google Scholar 

  2. V. F. Babenko,Extremal Problems of the Theory of Approximation and Nonsymmetric Norms [in Russian], Doctoral Degree Thesis (Physics and Mathematics), Kiev (1989).

  3. V. F. Babenko and I. F. Zayats, “NonsymmetricL 1-approximations of vector functions,” in:Approximation of Functions and Summation of Series [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1991), pp. 4–7.

    Google Scholar 

  4. D. Jackson, “A general class of problems in approximation,”Amer. J. Math.,46, 215–234 (1924).

    Google Scholar 

  5. N. I. Akhiezer and M. G. Krein,Some Problems of Moment Theory [in Russian], GONTI, Khar'kov (1938).

    Google Scholar 

  6. P. V. Galkin, “On the uniqueness of an element of the best approximation for the mean continuous function by splines with fixed knots,”Mat. Zametki,15, No. 1, 3–14 (1974).

    Google Scholar 

  7. H. Strauss, “L 1-Approximation mit Splinefunktionen,”Int. Ser. Numer. Math.,26, 151–162 (1975).

    Google Scholar 

  8. H. Strauss, “Unicity of best one-sidedL 1-approximations,”Numer. Math.,40, No. 2, 229–243 (1982).

    Google Scholar 

  9. M. P. Carrol and D. Braess, “On uniqueness ofL 1-approximation for certain families of spline functions,”J. Approxim. Theory,12, No. 4, 362–364 (1974).

    Google Scholar 

  10. H. Strauss, “Eindeutigkeit in derL 1-approximation,”Math. Z.,176, 63–74 (1981).

    Google Scholar 

  11. T. V. Nakonechnaya, “Determining sets for asymmetric approximations inL 1,” in:Studies of Contemporary Problems of Summation and Approximation of Functions and Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1984), pp. 21–31

    Google Scholar 

  12. B. R. Kripke and T. I. Rivlin, “Approximation in the metric ofL 1 (X, μ),”Trans. Amer. Math. Soc.,119, No. 1, 101–122 (1965).

    Google Scholar 

  13. A. N. Kolmogorov and S. V. Fomin,Elements of Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  14. N. P. Korneichuk, A. A. Ligun, and V. G. Doronin,Approximation with Restrictions [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk University, Dnepropetrovsk

    V. F. Babenko & V. N. Glushko

Authors
  1. V. F. Babenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Glushko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 475–483, May, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babenko, V.F., Glushko, V.N. On the uniqueness of elements of the best approximation and the best one-sided approximation in the spaceL 1 . Ukr Math J 46, 503–513 (1994). https://doi.org/10.1007/BF01058514

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058514

Keywords

Search

Navigation