On a class of approximation operators

Abstract

In this note we construct a class of approximation operators using polynomial sequences of binomial type. We compute the expression of these operators on the test functions and we give a convergence theorem. We give also quantitative evaluations of the order of approximation by using the moduli of continuity of first and second order and we establish an integral representation of the remainder term in the case when the approximation formula has the degree of exactness one. Some special cases, almost all of them being studied previously by D.D. Stancu, are mentioned.

Authors

Maria Crăciun
”Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy

Keywords

positive approximation operators; polynomial sequences of binomial type; evaluation of remainder

References

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Paper coordinates

Maria Crăciun, On a class of approximation operators, Mathematical Sciences Research, 2005, pp. 292-303

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About this paper

Journal

Mathematical Sciences Research

Publisher Name

Global Publishing Company

DOI

Print ISSN

1537-5978

Online ISSN

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