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Abstrakty
In this paper, we prove a fuzzy Korovkin-type approximation theorem for fuzzy positive linear operators by using A-statistical convergence for four-dimensional summability matrices. Also, we obtain rates of A-statistical convergence of a double sequence of fuzzy positive linear operators for four-dimensional summability matrices.
Słowa kluczowe
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Czasopismo
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Tom
Strony
37--49
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Sinop University, Faculty of Arts and Sciences, Department of Mathematics, 57000, Sinop, Turkey
autor
- Sinop University, Faculty of Arts and Sciences, Department of Mathematics, 57000, Sinop, Turkey
Bibliografia
- [1] G. A. Anastassiou, Fuzzy approximation by fuzzy convolution type operators, Comput. Math. Appl. 48 (2004), 1369–1386.
- [2] G. A. Anastassiou, High-order fuzzy approximation by fuzzy wavelet type and neural network operators, Comput. Math. Appl. 48 (2004), 1387–1401.
- [3] G. A. Anastassiou, On basic fuzzy Korovkin theory, Stud. Univ. Babeş–Bolyai Math. 50 (2005), 3–10.
- [4] G. A. Anastassiou, Fuzzy random Korovkin theory and inequalities, Math. Inequal. Appl. 10 (2007), 63–94.
- [5] G. A. Anastassiou, O. Duman, Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl. 55 (2008), 573–580.
- [6] F. Dirik, K. Demirci, Four-dimensional matrix transformation and rate of A-statistical convergence of continuous functions, Comput. Math. Appl. 59 (2010), 2976–2981.
- [7] O. Duman, M. K. Khan, C. Orhan, A-statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), 689–699.
- [8] O. Duman, G. A. Anastassiou, On statistical fuzzy trigonometric Korovkin theory, J. Comput. Anal. Appl. 10 (2008), 333–344.
- [9] O. Duman, Fuzzy approximation based on statistical rates, Publ. Math. Debrecen 76 (4) (2010), 453–464.
- [10] S. G. Gal, Approximation theory in fuzzy setting, in: Handbook of Analytic-Computational Methods in Applied Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2000, 617–666.
- [11] R. J. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18 (1986), 31–43.
- [12] H. J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), 29–60.
- [13] G. H. Hardy, Divergent Series, Oxford Univ. Press, London, 1949.
- [14] Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
- [15] F. Moricz, Statistical convergence of multiple sequences, Arch. Math. (Basel) 81 (2004), 82–89.
- [16] A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53 (1900), 289–321.
- [17] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Transl. 28 (1926), 50–73.
- [18] C. X. Wu, M. Ma, Embedding problem of fuzzy number space I, Fuzzy Sets and Systems 44 (1991), 33–38.
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Bibliografia
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