Approximation of Urison operator with operator polynomials of Stancu type

TL;DR

This paper investigates positive polynomial operators that approximate the Urison operator on a regular triangle, deriving Bernstein polynomials as a special case, thus expanding approximation techniques for integral operators.

Contribution

It introduces a new class of positive polynomial operators for Urison approximation and shows how Bernstein polynomials are a specific instance.

Findings

Established a positive polynomial operator approximating Urison operator on a triangle.

Derived Bernstein polynomials as a particular case of the proposed operators.

Enhanced understanding of polynomial approximation for integral operators.

Abstract

Positive polynomial operator that approximates Urison operator, when integration domain is a "regular triangle" is investigated. We obtain Bernstein Polynomials as a particular case.