Skip to main content

On the Generalized Favard-Kantorovich and Favard-Durrmeyer Operators in Exponential Function Spaces

Abstract

We consider the Kantorovich- and the Durrmeyer-type modifications of the generalized Favard operators and we prove an inverse approximation theorem for functions such that, where and,.

[12345678910]

References

  1. 1.

    Gawronski W, Stadtmüller U: Approximation of continuous functions by generalized Favard operators. Journal of Approximation Theory 1982,34(4):384–396. 10.1016/0021-9045(82)90081-8

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Favard J: Sur les multiplicateurs d'interpolation. Journal de Mathématiques Pures et Appliquées 1944, 23: 219–247.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Becker M, Butzer PL, Nessel RJ: Saturation for Favard operators in weighted function spaces. Studia Mathematica 1976,59(2):139–153.

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Becker M: Inverse theorems for Favard operators in polynomial weight spaces. Commentationes Mathematicae 1980/81,22(2):165–173.

    MathSciNet  Google Scholar 

  5. 5.

    Pych-Taberska P: On the generalized Favard operators. Functiones et Approximatio Commentarii Mathematici 1998, 26: 265–273.

    MathSciNet  MATH  Google Scholar 

  6. 6.

    Pych-Taberska P, Nowak G: Approximation properties of the generalized Favard-Kantorovich operators. Commentationes Mathematicae 1999, 39: 139–152.

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Nowak G, Pych-Taberska P: Some properties of the generalized Favard-Durrmeyer operators. Functiones et Approximatio Commentarii Mathematici 2001, 29: 103–112.

    MathSciNet  Google Scholar 

  8. 8.

    Anastassiou GA, Cottin C, Gonska HH: Global smoothness of approximating functions. Analysis 1991,11(1):43–57.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Nowak G: Direct theorems for generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces. to appear in Ukrainian Mathematical Journal to appear in Ukrainian Mathematical Journal

  10. 10.

    Kratz W, Stadtmüller U: On the uniform modulus of continuity of certain discrete approximation operators. Journal of Approximation Theory 1988,54(3):326–337. 10.1016/0021-9045(88)90009-3

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Grzegorz Nowak.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Nowak, G., Sikorska-Nowak, A. On the Generalized Favard-Kantorovich and Favard-Durrmeyer Operators in Exponential Function Spaces. J Inequal Appl 2007, 075142 (2008). https://doi.org/10.1155/2007/75142

Download citation

Keywords

  • Exponential Function
  • Function Space
  • Approximation Theorem
  • Inverse Approximation
  • Exponential Function Space
\