Statistical approximation properties of the Durrmeyer type q-Bleimann, Butzer, and Hahn operators

摘要

In this paper, we introduce a Durrmeyer-type generalization of q-Bleimann, Butzer, and Hahn operators based on q-integers and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. We also compute rates of statistical convergence of these q-type operators by means of the modulus of continuity and Lipschitz-type maximal function, respectively.