Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 75142, 12 pages
doi:10.1155/2007/75142
Research Article
On the Generalized Favard-Kantorovich and Favard-Durrmeyer Operators in Exponential Function Spaces
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.
Abstract
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 wσf∈Lp(R), where 1≤p≤∞
and wσ(x)=exp(−σx2), σ>0.