Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6656
Title: Equi-statistical convergence of positive linear operators
Authors: Karakuş, Sevda
Demirci, Kamil
Duman, Oktay
Keywords: statistical convergence
equi-statistical convergence
Korovkin-type approximation theorem
Bernstein polynomials
Voronovskaya-type theorem
modulus of continuity
Issue Date: 2008
Publisher: Academic Press Inc Elsevier Science
Abstract: Balcerzak, Dems and Komisarski [M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007) 715-729] have recently introduced the notion of equi-statistical convergence which is stronger than the statistical uniform convergence. In this paper we study its use in the Korovkin-type approximation theory. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. We also compute the rates of equi-statistical convergence of sequences of positive linear operators. Furthermore, we obtain a Voronovskaya-type theorem in the equi-statistical sense for a sequence of positive linear Operators constructed by means of the Bernstein polynomials. (C) 2007 Elsevier Inc. All rights reserved.
URI: https://doi.org/10.1016/j.jmaa.2007.07.050
https://hdl.handle.net/20.500.11851/6656
ISSN: 0022-247X
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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