On statistical fuzzy trigonometric Korovkin theory

Journal of Computational Analysis and Applications

Volumn 10, Issue 3, 2008, Pages 333-344

  Duman, Oktay ^a   Anastassiou, George A ^b  

^a TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY   (Turkey)

^b University of Memphis   (United States)

Author keywords

Fuzzy modulus of continuity; Fuzzy positive linear operators; Statistical convergence; Statistical rates; Trigonometric functions; Trigonometric fuzzy Korovkin theory

Indexed keywords

EID: 49149125244     PISSN: 15211398     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. O. Duman, Statistical approximation for periodic functions, Demonstratio Math. 36 (2003) 873-878.
2. O. Duman and E. Erkuş, Approximation of continuous periodic functions via statistical convergence, Comput. Math. Appl. 52 (2006) 967-974.
3. O. Duman, M.K. Khan, C. Orhan, A-Statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003) 689-699.
4. E. Erkuş and O. Duman, A-Statistical extension of the Korovkin type approximation theorem, Proc. Indian Acad. Sci. Math. Sci. 115 (2005) 499-508.
5. A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002) 129-138.
6. G.A. Anastassiou, Fuzzy random Korovkin theory and inequalities, Math. Inequal. Appl. 10 (2007) 63-94.
7. G.A. Anastassiou, On basic fuzzy Korovkin theory, Studia Univ. Babeş-Bolyai Math. 50 (2005) 3-10.
8. G.A. Anastassiou, Fuzzy approximation by fuzzy convolution type operators, Comput. Math. Appl. 48 (2004) 1369-1386.
9. G.A. Anastassiou and S.G. Gal, On fuzzy trigonometric Korovkin theory, Nonlinear Funct. Anal. Appl. 11 (2006) 385-395.
10. S.G. Gal, Approximation theory in fuzzy setting, Handbook of Analytic-Computational Methods in Applied Mathematics, 617-666, Chapman & Hall/CRC, Boca Raton, FL, 2000.
11. R.J. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18 (1986) 31-43.
12. C.X. Wu, M. Ma, Embedding problem of fuzzy number space I, Fuzzy Sets and Systems 44 (1991) 33-38.
13. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
14. J. Boos, Classical and Modern Methods in Summability, Oxford University Press, UK, 2000.
15. P.P. Korovkin, Linear Operators and Theory of Approximation, Hindustan Publ. Corp., Delhi, 1960.
16. A.R. Freedman, J.J. Sember, Densities and summability, Paci.c J. Math. 95 (1981) 293-305.
17. E. Kolk, Matrix summability of statistically convergent sequences, Analysis 13 (1993) 77-83.
18. J.A. Fridy, On statistical convergence, Analysis 5 (1985) 301-313.
19. H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995) 1811-1819.
20. F. Nuray, E. Savaş, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca 45 (1995) 269-273.
21. M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28 (1986) 28-37.
22. J.A. Fridy, Minimal rates of summability, Canad. J. Math. 30 (1978) 808-816.
23. J.A. Fridy, H.I. Miller and C. Orhan, Statistical rates of convergence, Acta Sci. Math. (Szeged) 69 (2003) 147-157.
24. H.I. Miller, Rates of convergence and topics in summability theory, Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka 22 (1983) 39-55.