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 $$(\lambda _n)_{n\ge 1}$$ such that $$\lim \limits _{n\rightarrow \infty }\lambda _n=0$$ , how fast we want. Particular cases are presented.