Document Type : Research Paper

Authors

• Dilek Soylemez ¹
• Mehmet Unver ²

¹ Department of Mathematics, Faculty of Science, Selcuk University, Selcuklu, 42003 Konya, Turkey

² Department of Mathematics, Faculty of Science, Ankara University, Besevler, 06100 Ankara, Turkey

Abstract

In this paper we investigate some Korovkin type approximation properties of the $q$-Meyer-König and Zeller operators and Durrmeyer variant of the $q$-Meyer-König and Zeller operators via Abel summability method which is a sequence-to-function transformation and which extends the ordinary convergence. We show that the approximation results obtained in this paper are more general than some previous results. We also obtain the rate of Abel convergence for the corresponding operators. Finally, we conclude our results with some graphical analysis.

Keywords

• Meyer-König and Zeller Operators
• Abel convergence
• rate of convergence