Voronovskaja-Type Quantitative Results for Differences of Positive Linear Operators

Ana Maria Acu,Ioan Raşa,Gülen Başcanbaz-Tunca

doi:10.3390/sym13081392

Abstract

We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating the theoretical aspects are presented.

Highlights

The problem of studying the differences of positive linear operators was formulated firstly by Lupas [1]
Rasa [4] noticed the advantages of the discrete operators associated with certain integral operators in this area
It is helpful to mention the work of Heilmann et al [5] from which the notion of discrete operator is reproduced below [2]: Let I ⊂ R denote an interval and H be a subspace of C(I) containing the monomials ei(x) = xi, i = 0, 1, 2

Summary

Introduction

The problem of studying the differences of positive linear operators was formulated firstly by Lupas [1]. The other approach considers those operators that have the same fundamental functions and different functionals in their construction (see [2,3]). Rasa [4] noticed the advantages of the discrete operators associated with certain integral operators in this area. In this sense, it is helpful to mention the work of Heilmann et al [5] from which the notion of discrete operator is reproduced below [2]: Let I ⊂ R denote an interval and H be a subspace of C(I) containing the monomials ei(x) = xi, i = 0, 1, 2. In [3], some useful estimates for the differences of certain positive linear operators with the same fundamental functions were studied. We study the difference of positive linear operators, with the same fundamental functions, by obtaining Voronovskaja-type quantitative estimates

Preliminaries

Conclusions