Approximation operators constructed by means of Sheffer sequences


  • Maria Crăciun Tiberiu Popoviciu Institute of Numerical Analysis


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


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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How to Cite

Crăciun, M. (2001). Approximation operators constructed by means of Sheffer sequences. Rev. Anal. Numér. Théor. Approx., 30(2), 135–150. Retrieved from