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Siberian Mathematical Journal

, Volume 47, Issue 4, pp 696–709 | Cite as

An estimate for the least uniform deviation from the class of functions with bounded second derivative

  • A. V. Mironenko
Article

Abstract

We consider the problem of uniform approximation of a continuous function on an interval by means of the class of functions with bounded second derivative. We prove an estimate for the least uniform deviation of a function in terms of its local deviations on uniform and nonuniform three-point grids.

Keywords

uniform approximation bounded second derivative 

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References

  1. 1.
    Mironenko A. V., “Uniform approximation by a class of functions with a bounded derivative,” Math. Notes, 74, No. 5–6, 656–670 (2003).MathSciNetCrossRefGoogle Scholar
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    Korneichuk N. P., Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).Google Scholar
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    Shevchuk I. A., Approximation by polynomials and traces of continuous functions on an interval [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  4. 4.
    Dzyadyk V. K., Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. V. Mironenko
    • 1
  1. 1.Institute of Mathematics and MechanicsEkaterinburgRussia

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