Dirik, FadimeDemirci, Kamil2025-03-232025-03-2320090895-71771872-9479https://doi.org/10.1016/j.mcm.2008.11.002https://hdl.handle.net/11486/6454In this paper, using the concept of B-statistical convergence for sequence of infinite matrices B = (B-i) with B-i = (b(nk)(i)) we investigate various approximation results concerning the classical Korovkin theorem. Then we present two examples of sequences of positive linear operators. The first one shows that the statistical Korovkin type theorem does not work but our approximation theorem works. The second one gives that our approximation theorem does not work but the statistical Korovkin type theorem works. Also, we study the rates of B-statistical convergence of approximating positive linear operators and give a Voronovskaya-type theorem. (C) 2009 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessB-statistical convergence of sequenceKorovkin-type approximation theoremBernstein polynomialsModulus of continuityVoronovskaya-type theoremArticle499-102037204410.1016/j.mcm.2008.11.0022-s2.0-63449107352N/AWOS:000264925300024N/A