# Approximation operators constructed by means of Sheffer sequences

## Abstract

In this paper we introduce a class of positive linear operators by using the “umbral calculus”, and we study some approximation properties of it.

Let $$Q$$ be a delta operator, and $$S$$ an invertible shift invariant operator.

For $$f\in C[0,1]$$ we define $$(L_{n}^{Q,S}f)(x)=\frac{1}{sn_{(1)}}\sum \limits_{k=0}^{n}\binomial{n}{k} p_{k}(x)s_{n-k}(1-x)f(\frac{k}{n})$$, where $$(p_{n})_{n\geq0}$$ is a binomial sequence which is the basic sequence for $$Q$$, and $$(s_{n})_{n\geq0}$$ is a Sheffer set, $$s_{n}=S^{-1}p_{n}$$.

These operators generalize the binomial operators of T. Popoviciu.

## Authors

Maria Craciun
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

approximation operators; Sheffer sequences; basic sequences; delta operators

## PDF

##### Cite this paper as:

M. Crăciun, Approximation operators constructed by means of Sheffer sequences, Rev. Anal. Numér. Théor. Approx., vol. 30 (2001), no. 2, 135-150

1222-9024

##### Online ISSN

2457-8126

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