Shape preserving properties of the Bernstein polynomials with integer coefficients

TL;DR

This paper investigates the shape-preserving properties of Bernstein polynomials with integer coefficients, establishing conditions for monotonicity and convexity preservation, and noting their asymptotic shape-preserving behavior.

Contribution

It provides new sufficient conditions for integer-coefficient Bernstein polynomials to preserve shape properties like monotonicity and convexity.

Findings

Sufficient conditions for shape preservation are identified.

Bernstein polynomials with integer coefficients are asymptotically shape preserving.

The paper clarifies when shape properties are maintained in integer-coefficient cases.

Abstract

The Bernstein polynomials with integer coefficients do not generally preserve monotonicity and convexity. We establish sufficient conditions under which they do. We also observe that they are asymptotically shape preserving.