ON ρ-STATISTICAL CONVERGENCE OF ORDER (α,β) FOR SEQUENCES OF FUZZY NUMBERS

Year 2023, , 96 - 103, 29.12.2023

Damla Barlak

https://doi.org/10.51477/mejs.1326338

Abstract

In this study, we first give the definition of ρ-statistical convergence of order (α,β) for sequences of fuzzy numbers. We also define the strongly w(ρ,F,q)-summable of order (α,β) and the strongly w(ρ,F,q,f)-summable of order (α,β), defined by a modulus function f for sequences of fuzzy numbers. Later we give some coverage theorems between these sets and the set S_α^β (ρ,F).

Keywords

Modulus function, Statistical convergence, Sequence of fuzzy numbers

References

• Fast, H., “Sur la convergence statistique”, Colloquium Math., 2, 241-244, 1951.
• Steinhaus, H., “Sur la convergence ordinaire et la convergence asymptotique”, Colloq. Math. 2, 73-74, 1951.
• Schoenberg, I.J., “The Integrability of Certain Functions and Related Summability Methods”, Amer. Math. Monthly, 66, 361-375, 1959.
• Aral, N. D., & Et, M., “Generalized difference sequence spaces of fractional order defined by Orlicz functions”, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 941-951, 2020.
• Aral, N.D., & Gunal, S., “On M_(λ_(m,n) )statistical convergence”, Journal of Mathematics, 1–8, 2020.
• Aral, N.D., & Kandemir, H. Ş., “I-lacunary statistical convergence of order β of difference sequences of fractional order”, Facta Univ. Ser. Math. Inform. 36 (1), 43—55, 2021.
• Şengül, H., Et, M., & Altin, Y., “f-lacunary statistical convergence and strong f-lacunary summability of order α of double sequences”, Facta Univ. Ser. Math. Inform. 35 (2), 495—506, 2020.
• Zadeh, L. A., “Fuzzy sets”, Inform and Control, 8, 338-353, 1965.
• Matloka, M., “Sequences of fuzzy numbers”, BUSEFAL, 28, 28-37, 1986.
• Nuray, F., Savaş, E., “Statistical convergence of sequences of fuzzy real numbers”, Math. Slovaca 45(3), 269-273, 1995.
• Kwon, J.S., “On statistical and p-Cesaro Convergence of fuzzy numbers”, Korean J. Comput. & Appl. Math., 7(1), 195-203, 2000.
• Gadjiev, A.D., Orhan, C., “Some approximation theorems via statistical convergence”, Rocky Mt J Math. 32(1),129–138, 2002.
• Çolak, R., “Statistical convergence of order α. Modern methods in analysis and its applications”, Anamaya Pub, New Delhi, 121–129, 2010.
• Şengül, H., “Some Cesàro-type summability spaces defined by a modulus function of order (α,β)”, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 66(2), 80—90, 2017.
• Altınok, H., & Et, M., “Statistical convergence of order (β,γ) for sequences of fuzzy numbers”, Soft Computing, 23, 6017-6022, 2019. doi:10.1007/s00500-018-3569-z
• Çakallı, H., “A variation on statistical ward continuity”, Bull. Malays. Math. Sci. Soc. 40, 1701-1710, 2017. doi:10.1007/s40840-015-0195-0
• Aral., N.D., “ρ-statistical convergence defined by modulus function of order (α, β)”, Maltepe Journal of Mathematics, 4(1), 15-23, 2022. doi:10.47087/mjm.1092599
• Kandemir, H.Ş., “On ρ-statistical convergence in topological groups”, Maltepe Journal of Mathematics, 4(1), 9-14, 2022. doi:10.47087/mjm.1092559
• Aral, N.D., Kandemir, H.Ş., Et. M., “On ρ− Statistical convergence of sequences of Sets”, Conference Proceeding Science and Tecnology, 3(1),156-159, 2020.
• Gumus, H., “Rho-statistical convergence of interval numbers”, International Conference on Mathematics and Its Applications in Science and Engineering. 2022.
• Aral, N.D., Kandemir, H., & Et, M., "On ρ−statistical convergence of order α of sequences of function", e-Journal of Analysis and Applied Mathematics, 2022(1), 45-55, 2022.
• Cakalli, H., Et, M., & Şengül, H., “A variation on N_θ- ward continuity”, Georgian Math. J. 27 (2), 191—197, 2020.
• Nakano, H., “Concave modulars”, J. Math. Soc. Japan, 5, 29-49, 1953.
• Maddox, I.J., “Spaces of strongly summable sequences”, The Quarterly Journal of Mathematics, 18(1), 345-355, 1967.