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.

Anahtar Kelimeler

Equi-statistical σ-convergence | Korovkin-type approximation theorem | Positive linear operator | Statistical pointwise σ-convergence | Statistical uniform σ-convergence

Science Direct

Atıf Sayıları
Web of Science	64
Scopus	61
Google Scholar	78

Equi statistical convergence of positive linear operators

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