From uniform to statistical convergence of binomial-type operators

Abstract

Sequences of binomial operators introduced by using umbral calculus are investigated from the point of view of statistical convergence. This approach is based on a detailed presentation of delta operators and their associated basic polynomials. Bernstein–Sheffer linear positive operators are analyzed, and some particular cases are highlighted: Cheney–Sharma operators, Stancu operators, Lupaş operators.

Authors

O. Agratini
(Babes-Bolyai University, Cluj-Napoca
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Keywords

Statistical convergence; Binomial sequence; Linear positive operator; Umbral calculus Bernstein–Sheffer operator; Pincherle derivative 

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Paper coordinates

O. Agratini, From uniform to statistical convergence of binomial-type operators, In: Advances In Summability And Approximation Theory, 169 – 179, (Eds. S. A. Mohiuddine, T. Acar), Springer, Singapore, 2018. ISBN: 978-981-13-3076-6, DOI https://doi.org/10.1007/978-981-13-3077-3_10

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