On mixed partial derivatives of modified Bernstein-Stancu polynomials for functions of several variables

TL;DR

This paper investigates how well modified Bernstein-Stancu polynomials can approximate second-order mixed partial derivatives of multivariable functions in the L1 norm, requiring minimal regularity conditions.

Contribution

It establishes approximation results for mixed partial derivatives of multivariable functions using modified Bernstein polynomials under minimal regularity.

Findings

Successful approximation of second-order mixed partial derivatives in L1 norm.

Minimal regularity conditions are sufficient for the approximation.

Provides theoretical foundation for using Bernstein polynomials in multivariable derivative approximation.

Abstract

The goal of the paper is establishing the approximation of mixed partial derivatives of the second order of a function of several variables via modified Bernstein polynomials in the $L_1$ norm under the minimal regularity.