Equi-statistical convergence of positive linear operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:339

Article

Karakus, Sevda¹  Demirci, Kamil¹  Duman, Oktay² 

[1] Ondokuz Mayis Univ, Fac Sci & Arts Sinop, Dept Math, TR-57000 Sinop, Turkey

[2] TOBB Econ & Technol Univ, Fac Arts & Sci, Dept Math, TR-06530 Ankara, Turkey

关键词: statistical convergence;    equi-statistical convergence;    Korovkin-type approximation theorem;    Bernstein polynomials;    Voronovskaya-type theorem;    modulus of continuity;   

DOI  :  10.1016/j.jmaa.2007.07.050

来源: Elsevier

【 摘 要 】

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.

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