Some approximation properties of Lupa\cs $q$-analogue of Bernstein operators

TL;DR

This paper investigates the convergence rates of Lupa extquotesingle s $q$-analogue Bernstein operators and establishes a quantitative version of Voronovskaja's theorem, enhancing understanding of their approximation properties.

Contribution

It provides new quantitative convergence results and a variant of Voronovskaja's theorem for Lupa extquotesingle s $q$-analogue Bernstein operators.

Findings

Established convergence rates for $R_{n,q}$

Proved a quantitative Voronovskaja's theorem

Enhanced understanding of approximation properties

Abstract

In this paper, we discuss rates of convergence for the Lupa\c{s} $q$-analogue of Bernstein polynomials $R_{n,q}$. We prove a quantitative variant of Voronovskaja's theorem for $R_{n,q}$