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A Baskakov type generalization of statistical Korovkin theory. (English) Zbl 1133.41004
Summary: Using the notion of \(A\)-statistical convergence, where \(A\) is a nonnegative regular summability matrix, we obtain some statistical variants of Baskakov’s results on the Korovkin type approximation theorems.

MSC:
41A36 Approximation by positive operators
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[1] Baskakov, V.A., Generalization of certain theorems of P.P. Korovkin on positive operators, Mat. zametki, 13, 785-794, (1973), (in Russian) · Zbl 0278.43011
[2] Korovkin, P.P., Linear operators and theory of approximation, (1960), Hindustan Publ. Corp. Delhi · Zbl 0107.05302
[3] Duman, O.; Orhan, C., Statistical approximation by positive linear operators, Studia math., 161, 187-197, (2004) · Zbl 1049.41016
[4] Gadjiev, A.D.; Orhan, C., Some approximation theorems via statistical convergence, Rocky mountain J. math., 32, 129-138, (2002) · Zbl 1039.41018
[5] Erkuş, E.; Duman, O., A Korovkin type approximation theorem in statistical sense, Studia sci. math. hungar., 43, 285-294, (2006) · Zbl 1108.41012
[6] Fast, H., Sur la convergence statistique, Colloq. math., 2, 241-244, (1951) · Zbl 0044.33605
[7] Boos, J., Classical and modern methods in summability, (2000), Oxford Univ. Press UK · Zbl 0954.40001
[8] Freedman, A.R.; Sember, J.J., Densities and summability, Pacific J. math., 95, 293-305, (1981) · Zbl 0504.40002
[9] Hardy, G.H., Divergent series, (1949), Oxford Univ. Press London · Zbl 0032.05801
[10] Kolk, E., Matrix summability of statistically convergent sequences, Analysis, 13, 77-83, (1993) · Zbl 0801.40005
[11] Fridy, J.A., On statistical convergence, Analysis, 5, 301-313, (1985) · Zbl 0588.40001
[12] Miller, H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. amer. math. soc., 347, 1811-1819, (1995) · Zbl 0830.40002
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