In the present manuscript, we consider µ-Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, we prove a Voronovskaja type, quantitative Voronovskaja type and Grüss-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