Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render

TL;DR

This paper discusses a Bernstein-type operator introduced by Aldaz, Kounchev, and Render, providing new direct results using classical second order modulus and a modified approach inspired by Marsden and Schoenberg.

Contribution

It offers new direct results for the Bernstein-type operator, enhancing understanding through classical and modified modulus approaches.

Findings

New direct results in terms of second order modulus

Modified approach following Marsden and Schoenberg

Enhanced analysis of the Bernstein-type operator

Abstract

The Bernstein-type operator of Aldaz, Kounchev and Render (2009) is discussed. New direct results in terms of the classical second order modulus as well as in a modification following Marsden and Schoenberg are given.