On the Construction of q-Analogues for some Positive Linear Operators


Ersin Şimşek, Tuncay Tunç




In this paper, we propose a method based on generating functions for constructing q-analogues of some discrete type positive linear operators (e.g., q-Lupas, q-Bernstein, q-Meyer-König and Zeller and q-Bleimann-Butzer-Hahn operators etc.). In other words, general operators of the discrete type are constructed , and their respective formulae for central moments are thereby obtained. Finally, through the use of specific generating functions, we are able to provide some relevant exemplary applications of general operators.