Abstract
In the present manuscript, we consider ?-Bernstein-Durrmeyer operators
involving a strictly positive continuous function. Firstly, we prove a
Voronovskaja type, quantitative Voronovskaja type and Gr?ss-Voronovskaja
type asymptotic formula, the rate of convergence by means of the modulus of
continuity and for functions in a Lipschitz type space. Finally, we show
that the numerical examples which describe the validity of the theoretical
example and the effectiveness of the defined operators.