Note on the Modified q-Bernstein Polynomials

TL;DR

This paper introduces modified q-Bernstein polynomials that differ from existing versions, providing new recurrence relations and expanding the mathematical understanding of these polynomials.

Contribution

The paper proposes a new form of q-Bernstein polynomials and derives novel recurrence formulas for them.

Findings

Derived new recurrence relations for the modified q-Bernstein polynomials.

Established differences between the modified and original q-Bernstein polynomials.

Enhanced the theoretical framework of q-Bernstein polynomials.

Abstract

In the present paper, we propose the modified q-Bernstein polynomials of degree n, which are different q-Bernstein polynomials of Phillips(see [4]). From these the modified q-Bernstein polynomials of degree n, we derive some interesting recurrence formulae for the modified q-Bernstein polynomials.