Aldaz-Kounchev-Render operators and their approximation properties

TL;DR

This paper investigates the approximation capabilities of Aldaz-Kounchev-Render operators, demonstrating their superiority over classical Bernstein operators for certain functions, extending results to bivariate cases, and supporting findings with numerical examples.

Contribution

It introduces new approximation results for AKR operators, extending them to bivariate functions and comparing their performance with existing methods.

Findings

AKR operators outperform Bernstein operators for specific function classes

Extension of approximation results to bivariate functions on [0,1]^2

Numerical examples validate theoretical improvements

Abstract

The approximation properties of the Aldaz-Kounchev-Render (AKR) operators are discussed and classes of functions for which these operators approximate better than the classical Bernstein operators are described. The new results are then extended to the bivariate case on the square $[0,1]^2$ and compared with other existing results known in literature. Several numerical examples, illustrating the relevance and supporting the theoretical findings, are presented