# Approximation with arbitrary order by certain linear positive operators

## Abstract

This paper aims to highlight classes of linear positive operators of discrete and integral type for which the rates in approximation of continuous functions and in quantitative estimates in Voronovskaya type results are of an arbitrarily small order. The operators act on functions defined on unbounded intervals and we achieve the intended purpose by using a strictly decreasing positive sequence $$(\lambda _{n})_{n\geq1}$$ such that $$lim_{n\rightarrow\infty}$$ $$\lambda_{n}=0$$, how fast we want. Particular cases are presented.

## Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Linear and positive operator · Korovkin theorem · Voronovskaya type theorems · Modulus of continuity · Order of approximation

## Paper coordinates

O. Agratini, Approximation with arbitrary order by certain linear positive operators, Positivity, 22 (2018), pp. 1241-1254, https://doi.org/10.1007/s11117-018-0570-9

## PDF

Positivity

Springer

1385-1292
##### Online ISSN

1572-9281

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