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

Year 2022, , 76 - 82, 28.12.2022
https://doi.org/10.55195/jscai.1218844

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
https://doi.org/10.55195/jscai.1218844

Abstract

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.
There are 24 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mithat Kasap 0000-0002-2064-2823

Hıfsı Altınok This is me 0000-0001-7836-8946

Publication Date December 28, 2022
Submission Date December 14, 2022
Published in Issue Year 2022

Cite

APA Kasap, M., & Altınok, H. (2022). Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers. Journal of Soft Computing and Artificial Intelligence, 3(2), 76-82. https://doi.org/10.55195/jscai.1218844
AMA Kasap M, Altınok H. Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers. JSCAI. December 2022;3(2):76-82. doi:10.55195/jscai.1218844
Chicago Kasap, Mithat, and Hıfsı Altınok. “Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers”. Journal of Soft Computing and Artificial Intelligence 3, no. 2 (December 2022): 76-82. https://doi.org/10.55195/jscai.1218844.
EndNote Kasap M, Altınok H (December 1, 2022) Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers. Journal of Soft Computing and Artificial Intelligence 3 2 76–82.
IEEE M. Kasap and H. Altınok, “Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers”, JSCAI, vol. 3, no. 2, pp. 76–82, 2022, doi: 10.55195/jscai.1218844.
ISNAD Kasap, Mithat - Altınok, Hıfsı. “Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers”. Journal of Soft Computing and Artificial Intelligence 3/2 (December 2022), 76-82. https://doi.org/10.55195/jscai.1218844.
JAMA Kasap M, Altınok H. Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers. JSCAI. 2022;3:76–82.
MLA Kasap, Mithat and Hıfsı Altınok. “Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers”. Journal of Soft Computing and Artificial Intelligence, vol. 3, no. 2, 2022, pp. 76-82, doi:10.55195/jscai.1218844.
Vancouver Kasap M, Altınok H. Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers. JSCAI. 2022;3(2):76-82.