TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS

Selin Çınar

DOI Number
https://doi.org/10.22190/FUMI200309006C
First page
065
Last page
077

Abstract


In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compact
subset of the real two-dimensional space. Based upon this new convergence
method, we prove Korovkin-type approximation theorem. Finally, we give some further developments.

Keywords

positive linear operators, The double sequences, regular matrix, triangular A-statistical convergence, Korovkin theorem

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References


T. Acar, S.A. Mohiuddine Statistical: (C;1)(E;1) summability and Korovkins theorem, Filomat 30(2) (2016) 387-393.

C. Bardaro, A. Boccuto, K. Demirci, I. Mantellini, S. Orhan: Triangular A-statistical approximation by double sequences of positive linear operators. Results Math. 68 (2015), 271-291.

C. Bardaro, A. Boccuto, K. Demirci, I. Mantellini, S. Orhan: Korovkin-

type theorems for modular Psi-A-statistical convergence. J. Funct. Spaces Article ID 160401, 2015 (2015), p. 11.

C. Bardaro and I. Mantellini: Korovkin's theorem in modular spaces. Commentationes Math. 47 (2007), 239-253.

C. Bardaro and I. Mantellini: A Korovkin Theorem in multivariate modular function spaces. J. Funct. Spaces Appl. 7 (2009), 105-120.

C. Belen, S.A. Mohiuddine: Generalized weighted statistical convergence and application, Appl. Math. Comput. 219 (2013), 9821-9826.

E. W. Chittenden: On the limit functions of sequences of continuous functions converging relatively uniformly. Trans. Amer. Math. Soc. 20 (1919), 179-184.

K. Demirci, F. Dirik: A Korovkin type approximation theorem for double sequences of positive linear operators of two variables in A-statistical sense. Bull. Korean Math. Soc. 47(4) (2010) 825-837.

K. Demirci, B. Kolay: A-Statistical Relative Modular Convergence of Positive Linear Operators. Positivity 21 (2017), 847863.

K. Demirci, S. Orhan: Statistical approximation by double sequences of positive linear operators on modular spaces. Positivity 19 (2015) 23-36.

K. Demirci, S. Orhan: Statistically relatively uniform convergence of positive linear operators. Results. Math. 69 (2016) 359-367.

K. Demirci, S. Orhan: Statistical relative approximation on modular spaces. Results. Math. 71 (2017) 1167-1184.

R. A. DeVore, G. G. Lorentz: Constructive Approximation ( Grund. Math. Wiss. 303). Springer Verlag, Berlin, 1993.

F. Dirik, K. Demirci: Korovkin-type approximation theorem for functions of two variables in statistical sense. Turk. J. Math. 34 (2010) 73-83.

K. Donner: Korovkin Theorems in Lp Spaces. J. Funct. Anal 42(1) (1981) 12-28.

S. M. Eisenberg: Korovkin's Theorem. Bull. Malays. Math. Soc. 2(2) (1979) 13-29.

H. Fast. Sur la Convergence Statistique. Colloq. Math. 2 (1951) 241-244.

P. Garrancho: A general Korovkin result under generalized convergence, Constr. Math. Anal., 2(2), (2019), 81-88.

A. D. Gadjiev, C. Orhan: Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32 (2002) 129-138.

U. Kadak, S.A. Mohiuddine: Generalized statistically almost convergence based on the di⁄erence operator which includes the (p;q)gamma function and related approximation theorems, Results Math. 73(1) (2018), Article9.

P. P. Korovkin: Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi, 1960.

E. H. Moore: An Introduction to a Form of General Analysis, The New Hawen Mathematical Colloquim, Yale University Press, New Hawen, 1910.

S.A. Mohiuddine: Statistical weighted Asummability with application to Korovkins type approximation theorem, J. Inequal. Appl. (2016) 2016:101.

S.A. Mohiuddine, B. A. S. Alamri: Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM 113(3) (2019) 1955-1973.

S.A. Mohiuddine, A. Asiri, B. Hazarika: Weighted statistical convergence through di⁄erence operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst. 48(5) (2019) 492-506.

S.A. Mohiuddine, B. Hazarika, M.A. Alghamdi: Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat 33(14) (2019) 4549-456.

F. Moricz: Statistical Convergence of multiple sequences. Arch. Math. 81(1) (2003) 82-89.

A. Pringsheim: Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 53 (1900) 289-321.

G. M. Robison: Divergent double sequences and series. Amer. Math. Soc. Transl. 28 (1926), 50-57.

H. Steinhaus: Sur la Convergence Ordinaire et la Convergence Asymptotique. Colloq. Math. 2 (1951) 73-74.

P. Şahin, F. Dirik: Statistical Relative Uniform Convergence of Double Sequence of Positive Linear Operators. Appl. Math. 17 (2017) 207-220.

T. O. Teoplitz: Uber allgemeine lineare Mittelbildungen. Prace Math. Fiz. 22 (1911) 113-119.

B. Yilmaz, K. Demirci, S. Orhan: Relative Modular Convergence of Positive Linear Operators. Positivity 20 (2016), 565-577.

D. E. Wulbert: Convergence of Operators and Korovkin's theorem. J. Approx. Theory 1 (1968) 381-390.




DOI: https://doi.org/10.22190/FUMI200309006C

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