Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 79410, 12 pages
doi:10.1155/2007/79410
Research Article
Bleimann, Butzer, and Hahn Operators Based on the q-Integers
1Department of Mathematics, Kirikkale University, Yahsihan, Kirikkale 71450, Turkey
2Department of Mathematics, Faculty of Sciences and Arts, Gazi University, Teknik Okullar, Ankara 06500, Turkey
Received 29 May 2007; Accepted 9 October 2007
Academic Editor: Ram N. Mohapatra
Copyright © 2007 Ali Aral 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 new generalization of Bleimann, Butzer, and Hahn operators, which includes q-integers. We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-type maximal function space. Finally, we de
fine a generalization of these new operators and study the uniform convergence of them.