×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[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.: 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: 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: 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.