Abstract
In this chapter, we present some Korovkin-type approximation theorems for functions of two variables via statistical convergence, A-statistical convergence, and statistical A-summability. We also study rates of A-statistical convergence of a double sequence of positive linear operators. Through some concrete examples, we show that the results present in this chapter are stronger than the classical results.
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References
F. Altomare, Korovkin-type theorems and approximation by positive linear operators. Surv. Approx. Theory 5, 92–164 (2010)
B.D. Boyanov, V.M. Veselinov, A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. Roum. 14(62), 9–13 (1970)
K. Demirci, F. Dirik, Four-dimensional matrix transformation and rate of A-statistical convergence of periodic functions. Math. Comput. Model. 52, 1858–1866 (2010)
K. Demirci, S. Karakuş, Statistical A-summability of positive linear operators. Math. Comput. Model. 49, 189–195 (2011)
K. Demirci, S. Karakuş, Korovkin-type approximation theorem for double sequences of positive linear operators via statistical A-summability. Results Math. 63, 1–13 (2013)
F. Dirik, K. Demirci, Korovkin-type approximation theorem for functions of two variables in statistical sense. Turk. J. Math. 34, 73–83 (2010)
O. Duman, E. Erkus, Approximation of continuous periodic functions via statistical convergence. Comput. Math. Appl. 52, 967–974 (2006)
M. Gurdek, L. Rempulska, M. Skorupka, The Baskakov operators for functions of two variables. Collect. Math. 50, 289–302 (1999)
P.P. Korovkin, Convergence of linear positive operators in the spaces of continuous functions. Dokl. Akad. Nauk SSSR (N.S.) 90, 961–964 (1953) (Russian)
P.P. Korovkin, Linear Operators and Approximation Theory (Hindustan Publ. Co., Delhi, 1960)
S.A. Mohiuddine, A. Alotaibi, Statistical convergence and approximation theorems for functions of two variables. J. Comput. Anal. Appl. 15(2), 218–223 (2013)
D.D. Stancu, A method for obtaining polynomials of Bernstein type of two variables. Am. Math. Mon. 70(3), 260–264 (1963)
V.I. Volkov, On the convergence of sequences of linear positive operators in the space of two variables. Dokl. Akad. Nauk SSSR 115, 17–19 (1957)
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Mursaleen, M., Mohiuddine, S.A. (2014). Statistical Approximation of Positive Linear Operators. In: Convergence Methods for Double Sequences and Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1611-7_8
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DOI: https://doi.org/10.1007/978-81-322-1611-7_8
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1610-0
Online ISBN: 978-81-322-1611-7
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