Advertisement

Ukrainian Mathematical Journal

, Volume 57, Issue 1, pp 52–69 | Cite as

Pointwise Estimates for the Coconvex Approximation of Differentiable Functions

  • H. A. Dzyubenko
  • V. D. Zalizko
Article
  • 19 Downloads

Abstract

We obtain pointwise estimates for the coconvex approximation of functions of the class W r , r > 3.

Keywords

Differentiable Function Pointwise Estimate Coconvex 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    G. A. Dzyubenko, J. Gilewicz, and I. A. Shevchuk, “Coconvex pointwise approximation,” Ukr. Mat. Zh., 54, No.9, 1200–1212 (2002).CrossRefGoogle Scholar
  2. 2.
    H. A. Dzyubenko and V. D. Zalizko, “Coconvex approximation of functions with more than one inflection point,” Ukr. Mat. Zh., 56, No.3, 352–365 (2004).Google Scholar
  3. 3.
    M. G. Pleshakov and A. V. Shatalina, “Piecewise coapproximation and the Whitney inequality,” Approxim. Theor., 105, 189–210 (2000).CrossRefGoogle Scholar
  4. 4.
    D. Leviatan and I. A. Shevchuk, “Coconvex approximation,” Approxim. Theor., 118, 20–65 (2002).CrossRefGoogle Scholar
  5. 5.
    K. A. Kopotun, “Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials,” Constr. Approxim., 10, 153–178 (1994).CrossRefGoogle Scholar
  6. 6.
    I. A. Shevchuk, Polynomial Approximation and Traces of Functions Continuous on a Segment [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  7. 7.
    A. S. Shvedov, “Orders of coapproximations of functions by algebraic polynomials,” Mat. Zametki, 30, 839–846 (1981).Google Scholar
  8. 8.
    X. Wu and S. P. Zhou, “A counterexample in comonotone approximation in L p space,” Colloq. Math., 64, 265–274 (1993).Google Scholar
  9. 9.
    I. A. Shevchuk, “Approximation of monotone functions by monotone polynomials,” Mat. Sb., 183, 63–78 (1992).Google Scholar
  10. 10.
    G. A. Dzyubenko, J. Gilewicz, and I. A. Shevchuk, “Piecewise monotone pointwise approximation,” Constr. Approxim., 14, 311–348 (1998).CrossRefGoogle Scholar
  11. 11.
    R. A. de Vore, “Monotone approximation by polynomials,” SIAM J. Math. Anal., 8, 906–921 (1977).CrossRefGoogle Scholar
  12. 12.
    V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar
  13. 13.
    R. A. de Vore and X. M. Yu, “Pointwise estimates for monotone polynomial approximation,” Constr. Approxim., 1, 323–331 (1985).CrossRefGoogle Scholar
  14. 14.
    V. K. Dzyadyk, “On the constructive characteristic of functions satisfying the condition (Lip α (0 < α < 1)) on a finite segment of the real axis,” Izv. Akad. Nauk SSSR, Ser. Mat., 20, No.2, 623–642 (1956).Google Scholar
  15. 15.
    H. Whitney, “On functions with bounded nth differences,” J. Math. Pures Appl., 8, No.36, 67–95 (1957).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • H. A. Dzyubenko
    • 1
  • V. D. Zalizko
    • 2
  1. 1.International Mathematical CenterUkrainian National Academy of SciencesKyivUkraine
  2. 2.National Pedagogic UniversityKyivUkraine

Personalised recommendations