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Positivity

, Volume 22, Issue 5, pp 1241–1254 | Cite as

Approximation with arbitrary order by certain linear positive operators

  • Octavian Agratini
Article
  • 70 Downloads

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 \((\lambda _n)_{n\ge 1}\) such that \(\lim \limits _{n\rightarrow \infty }\lambda _n=0\), how fast we want. Particular cases are presented.

Keywords

Linear and positive operator Korovkin theorem Voronovskaya type theorems Modulus of continuity Order of approximation 

Mathematics Subject Classification

41A36 41A25 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Babeş-Bolyai University, Faculty of Mathematics and Computer ScienceCluj-NapocaRomania

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