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Ukrainian Mathematical Journal

, Volume 64, Issue 11, pp 1780–1783 | Cite as

On rational functions of the best nonsymmetric approximations in integral metrics

  • O. V. Polyakov
  • N. O. Ruchaevskaya
Article

We obtain theorems that characterize the degree of the rational function of the best (α; β) -approximation in the space L p and conditions under which the value of the best rational (α; β) -approximation is less than the best (α; β) -approximation by algebraic polynomials.

Keywords

Lower Bound Rational Function Integrable Function Approximation Theory Mathematical Journal 
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.
    B. F. Babenko, “Nonsymmetric approximations in spaces of integrable functions,” Ukr. Mat. Zh., 34, No. 4, 409–416 (1982); English translation: Ukr. Math. J., 34, No. 4, 331–336 (1982).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).Google Scholar
  3. 3.
    A. K. Ramazanov, “On rational functions of the best approximation in integral metrics,” Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 5, 43–48 (1982).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • O. V. Polyakov
    • 1
  • N. O. Ruchaevskaya
    • 1
  1. 1.Dnepropetrovsk National UniversityDnepropetrovskUkraine

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