Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers

Abstract

In this article, we investigate the idea of Δ_λ^m-statistical boundedness of order β for sequences of fuzzy numbers. Additionally, we provide different inclusion relations between Δ_λ^m-statistical boundedness of order β and Δ_λ^m-statistical convergence of order β.

Keywords

• Fuzzy number
• Statistical boundedness
• Statistical convergence

References

1. H. Altınok, Statistical convergence of order β for generalized difference sequences of fuzzy numbers, J.Intell. Fuzzy Systems, c.26, ss.847-856, 2014.
2. H. Altınok and M. Et, On λ-Statistical boundedness of order β of sequences of fuzzy numbers, Soft Computing, c.19, s.8, ss. 2095-2100, 2015.
3. H. Altınok and M. Mursaleen, ∆-Statistical boundedness for sequences of fuzzy numbers, Taiwanese Journal of Mathematics, c.15, s.5, ss. 2081-2093, 2011.
4. S. Aytar and S. Pehlivan, statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., c.176, s.6, ss. 734-744, 2006.
5. V.K. Bhardwarj and I. Bala, On weak statistical convergence, Int. J. Math. Sci. Art. ID 38530, 9 pp., 2007.
6. V.K. Bhardwaj and S. Gupta, On some generalizations of statistical boundedness, J. Inequal. c.2014, s.12, 2014.
7. R. Çolak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, Yeni Delhi, India: Anamaya Pub, ss. 121-129, 2010.
8. R. Çolak and Ç.A. Bektaş, λ-Statistical convergence of order α, Acta Math. Sin. Engl. Ser. c. 31, sy 3, ss. 953-959, 2011.

9. J. S. Connor, The statistical and strong p- Cesaro convergence of sequences, Analysis, c. 8, ss. 47-63, 1988.
10. M. Et, strongly almost summable difference sequences of order m defined by a modulus, Studia Sci. Math. Hungar c. 40, sy 4, ss. 463-476, 2003.
11. M. Et and R. Çolak On some generalized difference sequence spaces, Soochow J. Math. c. 21, sy 4, ss. 377-386, 1995.
12. H. Fast, Sur la convergence statistique, Colloq. Math., sy 2, ss. 241-244, 1951.
13. J. Fridy, On statistical convergence, Analysis, sy 5, ss. 301-313, 1985.
14. J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., c. 125, sy 12, ss. 3625-3631, 1997.
15. A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. c. 32, sy 1, ss. 129-138, 2002.
16. H. Kızmaz, On certain sequences spaces, Canadian Math. Bull., c. 24, ss. 169-176, 1981.
17. M. Matloka, Sequences of fuzzy numbers, BUSEFAL, c. 28, ss. 28-37, 1986.
18. S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal. Art. ID 719729, 9 pp., 2012.
19. M. Mursaleen, λ-Statistical convergence, Math. Slovaca, c. 50, sy 1, ss. 111-115, 2000.
20. F. Nuray and E. Savaş, some new sequence spaces defined by a modulus function, Indian J. Pure Appl. Math. c. 24, sy 11, ss. 657-663, 1993.
21. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, c. 66, ss. 361-375, 1959.
22. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, c. 30, ss. 139-150, 1980.
23. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. c. 2, ss. 73-74, 1951.
24. L. A. Zadeh, Fuzzy sets, Information and Control c. 8, ss. 338-353, 1965.