International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 37253, 5 pages
doi:10.1155/IJMMS/2006/37253

Approximation of bounded variation functions by a Bézier variant of the Bleimann, Butzer, and Hahn operators

Vijay Gupta1 and Ogün Doğru2

1School of Applied Sciences, Netaji Subhas Institute of Technology, Sector-3, Dwarka, New Delhi 110045, India
2Department of Mathematics, Faculty of Science, Ankara University, Tandogan, Ankara 06100, Turkey

Received 21 March 2005; Revised 13 May 2006; Accepted 28 May 2006

Copyright © 2006 Vijay Gupta and Ogün Doğru. 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 give a sharp estimate on the rate of convergence for the Bézier variant of Bleimann, Butzer, and Hahn operators for functions of bounded variation. We consider the case when α≥1 and our result improves the recently established results of Srivastava and Gupta (2005) and de la Cal and Gupta (2005).