Open Access

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

Journal of Inequalities and Applications20082007:075142

Received: 18 January 2007

Accepted: 14 November 2007

Published: 9 January 2008


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 , .


Authors’ Affiliations

Higher School of Marketing and Management, Leszno, Poland
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland


  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)90081-8MathSciNetView ArticleMATHGoogle Scholar
  2. Favard J: Sur les multiplicateurs d'interpolation. Journal de Mathématiques Pures et Appliquées 1944, 23: 219–247.MathSciNetMATHGoogle Scholar
  3. Becker M, Butzer PL, Nessel RJ: Saturation for Favard operators in weighted function spaces. Studia Mathematica 1976,59(2):139–153.MathSciNetMATHGoogle Scholar
  4. Becker M: Inverse theorems for Favard operators in polynomial weight spaces. Commentationes Mathematicae 1980/81,22(2):165–173.MathSciNetGoogle Scholar
  5. Pych-Taberska P: On the generalized Favard operators. Functiones et Approximatio Commentarii Mathematici 1998, 26: 265–273.MathSciNetMATHGoogle Scholar
  6. Pych-Taberska P, Nowak G: Approximation properties of the generalized Favard-Kantorovich operators. Commentationes Mathematicae 1999, 39: 139–152.MathSciNetMATHGoogle Scholar
  7. Nowak G, Pych-Taberska P: Some properties of the generalized Favard-Durrmeyer operators. Functiones et Approximatio Commentarii Mathematici 2001, 29: 103–112.MathSciNetGoogle Scholar
  8. Anastassiou GA, Cottin C, Gonska HH: Global smoothness of approximating functions. Analysis 1991,11(1):43–57.MathSciNetView ArticleMATHGoogle 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 JournalGoogle Scholar
  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)90009-3MathSciNetView ArticleMATHGoogle Scholar


© G. Nowak and A. Sikorska-Nowak 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.