Brass-Stancu-Kantorovich Operators on a Hypercube

TL;DR

This paper introduces multivariate Brass-Stancu-Kantorovich operators on a hypercube, providing theoretical approximation results and error estimates in $L^{p}$ spaces for Lebesgue integrable functions.

Contribution

It extends the theory of Brass-Stancu-Kantorovich operators to multivariate settings on hypercubes, with new $L^{p}$-approximation and error estimation results.

Findings

Proved $L^{p}$-approximation properties for the operators.

Derived error estimates using multivariate moduli of continuity.

Established bounds in terms of $L^{p}$-norms for approximation errors.

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.