Brass-Stancu-Kantorovich Operators on a Hypercube

Abstract

We deal with multivariate Brass-Stancu-Kantorovich operators depending on a non-negative integer parameter and defined on the space of all Lebesgue integrable functions on a unit hypercube. We prove $L^p$-approximation and provide estimates for the $L^p$-norm of the error of approximation in terms of a multivariate averaged modulus of continuity and of the corresponding $L^p$-modulus.