Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 75142, 12 pages
Research Article

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

Grzegorz Nowak1 and Aneta Sikorska-Nowak2

1Higher School of Marketing and Management, Ostroroga 9a, Leszno 64-100, Poland
2Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań 61-614, Poland

Received 18 January 2007; Revised 12 June 2007; Accepted 14 November 2007

Academic Editor: Ulrich Abel

Copyright © 2007 Grzegorz Nowak and Aneta Sikorska-Nowak. 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.


We consider the Kantorovich- and the Durrmeyer-type modifications of the generalized Favard operators and we prove an inverse approximation theorem for functions f such that wσfLp(R), where 1p and wσ(x)=exp(σx2), σ>0.