Equi-statistical convergence of positive linear operators
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Tarih
2008
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Academic Press Inc Elsevier Science
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
statistical convergence, equi-statistical convergence, Korovkin-type approximation theorem, Bernstein polynomials, Voronovskaya-type theorem, modulus of continuity
Kaynak
Journal of Mathematical Analysis and Applications
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
339
Sayı
2
