A generalization of Bernstein-Durrmeyer operators on hypercubes by means of an arbitrary measure

In this paper we introduce and study a sequence of Bernstein- Durrmeyer type operators (Mn,μ)n≥1, acting on spaces of continuous or integrable functions on the multi-dimensional hypercube Qd of Rd (d ≥ 1), defined by means of an arbitrary measure μ. We investigate their approximation properties both in the space of all continuous functions and in Lp-spaces with respect to μ, also furnishing some estimates of the rate of convergence. Further, we prove an asymptotic formula for the Mn,μ's. The paper ends with a concrete example.