Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 79410, 12 pages
Research Article

Bleimann, Butzer, and Hahn Operators Based on the q-Integers

Ali Aral1 and Ogün Doğru2

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.


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.