International Journal of Nonlinear Analysis and Applications

New results on fractional difference triple sequences of fuzzy numbers

Articles in Press

Document Type : Research Paper

Authors

1 I.E.D. Camilo Torres Tenorio, Barranquilla, Colombia

2 Department of Mathematics, Tripura University, Agartala, 799022, Tripura, India

3 Department of Education (ITEP), NIT Agartala, Jirania, 799046, Tripura, India

4 Department of Mathematics, Tripura University, Tripura, India

10.22075/ijnaa.2021.25038.2892

Abstract

In this paper, we introduce triple sequence spaces of fuzzy numbers defined using the fractional difference operator and Musielak-Orlicz function. Besides, some topological properties for these spaces are shown and some inclusion relations are proved. Additionally, we define and prove theorems related to η-dual space of these spaces of fuzzy numbers.

Keywords

[1] H. Altinok, R. Colak, and M. Et, λ-difference sequence spaces of fuzzy numbers, Fuzzy Sets Syst. 160 (2009), no. 21, 3128–3139.
[2] P. Baliarsingh, A unifying approach to the difference operators and their applications, Bol. Soc. Parana. Mat. 33 (2013), no. 1, 49–56.
[3] P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput. 219 (2013), no. 18, 9737–9742.
[4] P. Baliarsingh, On difference double sequence spaces of fractional order, Indian J. Math. 58 (2016), no. 3, 287–310.
[5] P.Baliarsingh, On a fractional difference operator, Alexandria Eng. J. 55 (2016), no. 2, 1811–1816.
[6] P. Baliarsingh, On double difference operators via four dimensional matrices, J. Indian Math. Soc. 83 (2016), no. 3-4, 209–219.
[7] P. Baliarsingh and S. Dutta, On the classes of fractional order difference sequence spaces and their matrix trans[1]formations, Appl. Math. Comput. 250 (2015), 665–674.
[8] P. Baliarsingh and L. Nayak, Anote on fractional difference operators, Alexandria. Eng. J. 57 (2018), no. 2, 1051–1054.
[9] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets Syst. 35 (1990)), no. 2, 241–249.
[10] H. Dutta, Generalized difference sequence spaces defined by Orlicz functions and their Kothe-Toeplitz and null duals. Thai J. Math. 8 (2012), no. 1, 11–19.
[11] M. Et, E. Savas, and H. Altınok, On some difference sequence spaces of fuzzy numbers, Soft Comput. 20 (2016), no. 11, 4395–4401.
[12] S. Gahler, 2-metric spaces and their topological structure, Math. Nachr. 26 (1963), no. 1-4, 115–148.
[13] C. Granados, A generalization of the strongly Cesaro ideal convergence through double sequence spaces, Int. J. Appl. Math. 34 (2021), no. 3, 525–533.
[14] C. Granados, New notion of triple sequences on ideal spaces in metric spaces, Adv. Theory Nonlinear Anal. Appl. 5 (2021), no. 3, 363–368.
[15] C. Granados and A. Dhital, Statistical convergence of double sequences in neutrosophic normed spaces, Neutrosophic Sets Syst. 42 (2021), 333–344.
[16] A. Indumathi, N. Subramanian, and B. Hazarika, On the Borel summability method for convergence of triple sequences of Bernstein-Stancu operators of fuzzy numbers, Soft Comput. 25 (2021), 683–697.
[17] P. Kumar, V. Kumar, and S.S. Bhatia, Multiple sequences of fuzzy numbers and their statistical convergence, Math. Sci. 6 (2012), no. 2, 1–7.
[18] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Isr. J. Math. 10 (1971), no. 3, 379–390.
[19] E. Malkowsky, M. Mursaleen, and S. Suantai, The dual spaces of sets of difference sequences of order m and matrix transformations, Acta Math. Sin. Engl. Ser. 23 (2007), no. 3, 521–532.
[20] S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets Syst. 33 (1989), no. 1, 123–126.
[21] A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53 (1900), no. 3, 289–321.
[22] S. Saha and S. Roy, New classes of statistically pre-Cauchy triple sequences of fuzzy numbers defined by Orlicz function, J. Math. Soc. 85 (2018), no. 3-4, 411–421.
[23] E. Savas and M. Gurdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst. 27 (2014), no. 4, 1621–1629.
[24] P. Sharma, Fractional difference double sequences of fuzzy numbers, Afrika Mate. 32 (2021), no. 7, 1465–1473.
[25] S.K. Singh, S. Mishra, and P. Sharma, On difference double sequences of fractional order, AIP Conf. Proc. 1860, AIP Publishing LLC, Melville, 2017, pp. 020028-020031.
[26] B.C. Tripathy and B. Sarma, On some classes of difference double sequence spaces, Fasc. Math. 41 (2009), 135–142.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 11 January 2025
  • Receive Date: 28 August 2021
  • Accept Date: 22 November 2021