Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers
Year 2022,
, 76 - 82, 28.12.2022
Mithat Kasap
,
Hıfsı Altınok
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.
References
- H. Altınok, Statistical convergence of order β for generalized difference sequences of fuzzy numbers, J.Intell. Fuzzy Systems, c.26, ss.847-856, 2014.
- 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.
- H. Altınok and M. Mursaleen, ∆-Statistical boundedness for sequences of fuzzy numbers, Taiwanese Journal of Mathematics, c.15, s.5, ss. 2081-2093, 2011.
- S. Aytar and S. Pehlivan, statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., c.176, s.6, ss. 734-744, 2006.
- V.K. Bhardwarj and I. Bala, On weak statistical convergence, Int. J. Math. Sci. Art. ID 38530, 9 pp., 2007.
- V.K. Bhardwaj and S. Gupta, On some generalizations of statistical boundedness, J. Inequal. c.2014, s.12, 2014.
- R. Çolak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, Yeni Delhi, India: Anamaya Pub, ss. 121-129, 2010.
- 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.
- J. S. Connor, The statistical and strong p- Cesaro convergence of sequences, Analysis, c. 8, ss. 47-63, 1988.
- 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.
- M. Et and R. Çolak On some generalized difference sequence spaces, Soochow J. Math. c. 21, sy 4, ss. 377-386, 1995.
- H. Fast, Sur la convergence statistique, Colloq. Math., sy 2, ss. 241-244, 1951.
- J. Fridy, On statistical convergence, Analysis, sy 5, ss. 301-313, 1985.
- J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., c. 125, sy 12, ss. 3625-3631, 1997.
- A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. c. 32, sy 1, ss. 129-138, 2002.
- H. Kızmaz, On certain sequences spaces, Canadian Math. Bull., c. 24, ss. 169-176, 1981.
- M. Matloka, Sequences of fuzzy numbers, BUSEFAL, c. 28, ss. 28-37, 1986.
- 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.
- M. Mursaleen, λ-Statistical convergence, Math. Slovaca, c. 50, sy 1, ss. 111-115, 2000.
- 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.
- I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, c. 66, ss. 361-375, 1959.
- T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, c. 30, ss. 139-150, 1980.
- H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. c. 2, ss. 73-74, 1951.
- L. A. Zadeh, Fuzzy sets, Information and Control c. 8, ss. 338-353, 1965.
Year 2022,
, 76 - 82, 28.12.2022
Mithat Kasap
,
Hıfsı Altınok
References
- H. Altınok, Statistical convergence of order β for generalized difference sequences of fuzzy numbers, J.Intell. Fuzzy Systems, c.26, ss.847-856, 2014.
- 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.
- H. Altınok and M. Mursaleen, ∆-Statistical boundedness for sequences of fuzzy numbers, Taiwanese Journal of Mathematics, c.15, s.5, ss. 2081-2093, 2011.
- S. Aytar and S. Pehlivan, statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., c.176, s.6, ss. 734-744, 2006.
- V.K. Bhardwarj and I. Bala, On weak statistical convergence, Int. J. Math. Sci. Art. ID 38530, 9 pp., 2007.
- V.K. Bhardwaj and S. Gupta, On some generalizations of statistical boundedness, J. Inequal. c.2014, s.12, 2014.
- R. Çolak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, Yeni Delhi, India: Anamaya Pub, ss. 121-129, 2010.
- 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.
- J. S. Connor, The statistical and strong p- Cesaro convergence of sequences, Analysis, c. 8, ss. 47-63, 1988.
- 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.
- M. Et and R. Çolak On some generalized difference sequence spaces, Soochow J. Math. c. 21, sy 4, ss. 377-386, 1995.
- H. Fast, Sur la convergence statistique, Colloq. Math., sy 2, ss. 241-244, 1951.
- J. Fridy, On statistical convergence, Analysis, sy 5, ss. 301-313, 1985.
- J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., c. 125, sy 12, ss. 3625-3631, 1997.
- A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. c. 32, sy 1, ss. 129-138, 2002.
- H. Kızmaz, On certain sequences spaces, Canadian Math. Bull., c. 24, ss. 169-176, 1981.
- M. Matloka, Sequences of fuzzy numbers, BUSEFAL, c. 28, ss. 28-37, 1986.
- 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.
- M. Mursaleen, λ-Statistical convergence, Math. Slovaca, c. 50, sy 1, ss. 111-115, 2000.
- 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.
- I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, c. 66, ss. 361-375, 1959.
- T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, c. 30, ss. 139-150, 1980.
- H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. c. 2, ss. 73-74, 1951.
- L. A. Zadeh, Fuzzy sets, Information and Control c. 8, ss. 338-353, 1965.