Abstract
This paper aims to highlight classes of linear positive operators of discrete and integral type for which the rates in approximation of continuous functions and in quantitative estimates in Voronovskaya type results are of an arbitrarily small order. The operators act on functions defined on unbounded intervals and we achieve the intended purpose by using a strictly decreasing positive sequence \((\lambda _{n})_{n\geq1}\) such that \(lim_{n\rightarrow\infty}\) \(\lambda_{n}=0\), how fast we want. Particular cases are presented.
Authors
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Linear and positive operator · Korovkin theorem · Voronovskaya type theorems · Modulus of continuity · Order of approximation
Paper coordinates
O. Agratini, Approximation with arbitrary order by certain linear positive operators, Positivity, 22 (2018), pp. 1241-1254, https://doi.org/10.1007/s11117-018-0570-9
requires subscription: https://doi.org/10.1007/s11117-018-0570-9
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1572-9281
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