Equi-statistical convergence of positive linear operators |
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Authors: | Sevda Karaku? Oktay Duman |
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Institution: | a Ondokuz May?s University, Faculty of Sciences and Arts Sinop, Department of Mathematics, 57000 Sinop, Turkey b TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Sö?ütözü 06530, Ankara, Turkey |
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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. |
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Keywords: | Statistical convergence Equi-statistical convergence Korovkin-type approximation theorem Bernstein polynomials Voronovskaya-type theorem Modulus of continuity |
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