A new Bernstein-type operator based on P\'olya's urn model with negative replacement

TL;DR

This paper introduces a novel Bernstein-type operator derived from Pólya's urn model with negative replacement, demonstrating improved approximation properties over classical Bernstein operators through theoretical and numerical analysis.

Contribution

The paper presents a new Bernstein-type operator based on Pólya's urn with negative replacement, enhancing approximation estimates compared to classical operators.

Findings

The new operator improves approximation estimates.

Numerical evidence shows better performance than classical Bernstein operators.

The operator is based on a Pólya's urn model with negative replacement.

Abstract

Using P\'{o}lya's urn model with negative replacement we introduce a new Bernstein-type operator and we show that the new operator improves upon the known estimates for the classical Bernstein operator. We also provide numerical evidence showing that the new operator gives a better approximation when compared to some other classical Bernstein-type operators.