Browse > Article
http://dx.doi.org/10.4134/BKMS.2012.49.4.851

STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREM  

Belen, Cemal (Department of Mathematics Faculty of Science Cumhuriyet University)
Mursaleen, Mohammad (Department of Mathematics Aligarh Muslim University)
Yildirim, Mustafa (Mustafa Yildirim Department of Mathematics Faculty of Science Cumhuriyet University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 851-861 More about this Journal
Abstract
In this paper, we define the notion of statistical A-summability for double sequences and find its relation with A-statistical convergence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore, through an example, it is shown that our theorem is stronger than classical and statistical cases.
Keywords
statistical convergence; statistical A-summability; Korovkin theorem; double sequence; positive linear operators;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
연도 인용수 순위
  • Reference
1 M. Mursaleen and O. H. H. Edely, Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl. 293 (2004), no. 2, 532-540.   DOI   ScienceOn
2 R. F. Patterson and E. Savas, Korovkin and Weierstrass approximation via lacunary statistical sequences, J. Math. Stat. 1 (2005), no. 2, 165-167.   DOI
3 J. Boos, Classical and Modern Methods in Summability, Oxford University Press, New York, 2000.
4 K. Demirci and S. Karakus, Statistical A-summability of positive linear operators, Math. Comput. Modelling 53 (2011), no. 1-2, 189-195.   DOI   ScienceOn
5 V. I. Volkov, On the convergence of sequences of linear positive operators in the space of continuous functions of two variables, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 17-19.
6 A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53 (1900), no. 3, 289-321.   DOI
7 G. M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926), no. 1, 50-73.   DOI   ScienceOn
8 D. D. Stancu, A method for obtaining polynomials of Bernstein type of two variables, Amer. Math. Monthly 70 (1963), no. 3, 260-264.   DOI   ScienceOn
9 O. Duman, E. Erkus, and V. Gupta, Statistical rates on the multivariate approximation theory, Math. Comput. Modelling 44 (2006), no. 9-10, 763-770.   DOI   ScienceOn
10 F. Dirik and K. Demirci, Korovkin-type approximation theorem for functions of two variables in statistical sense, Turkish J. Math. 34 (2010), no. 1, 73-83.
11 O. Duman, M. K. Khan, and C. Orhan, A-statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), no. 4, 689-699.
12 O. H. H. Edely and M. Mursaleen, On statistical A-summability, Math. Comput. Modelling 49 (2009), no. 3-4, 672-680.   DOI   ScienceOn
13 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
14 A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), no. 1, 129-138.   DOI   ScienceOn
15 H. J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), no. 1, 29-60.   DOI
16 G. H. Hardy, Divergent Series, Oxford Univ. Press, London, 1949.
17 P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
18 F. Moricz, Statistical convergence of multiple sequences, Arch. Math. (Basel) 81 (2003), no. 1, 82-89.   DOI
19 M. Mursaleen and O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), no. 1, 223-231.   DOI   ScienceOn