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

Journal of Inequalities and Applications volume 2007, Article number: 075142 (2008) Cite this article

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,.

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References

  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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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. 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

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Higher School of Marketing and Management, Ostroroga 9a, Leszno, 64-100, Poland

    Grzegorz Nowak

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań, 61-614, Poland

    Aneta Sikorska-Nowak

Authors
  1. Grzegorz Nowak
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  2. Aneta Sikorska-Nowak
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Correspondence to Grzegorz Nowak.

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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.

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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

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  • DOI: https://doi.org/10.1155/2007/75142

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