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

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

Recommended by Ulrich Abel

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.