# Approximation operators constructed by means of Sheffer sequences

## Authors

• Maria Crăciun Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

## Keywords:

positive linear operators, umbral calculus, delta operator, invertible shift invariant operator, binomial operators of T. Popoviciu, Sheffer sequences
Abstract views: 254

## 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 \begin{equation*} (L_{n}^{Q,S}f)(x)= {\textstyle\frac{1}{s_{n}(1)}} \sum\limits_{k=0}^{n}{\textstyle\binom{n}{k}}p_{k}(x)s_{n-k}(1-x)f\left( \tfrac{k}{n} \right), \end{equation*} 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.

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2001-08-01

## How to Cite

Crăciun, M. (2001). Approximation operators constructed by means of Sheffer sequences. Rev. Anal. Numér. Théor. Approx., 30(2), 135–150. https://doi.org/10.33993/jnaat302-692

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