Korean J. Math. Vol. 31 No. 3 (2023) pp.349-361
DOI: https://doi.org/10.11568/kjm.2023.31.3.349

On lacunary $\Delta^{m}$-statistical convergence of triple sequence in intuitionistic fuzzy n-normed space

Main Article Content

Asif Hussain Jan
Tanweer Jalal

Abstract

In this article, we construct lacunary $\Delta^m$-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary $\Delta^m$-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary $\Delta^m$-statistical Cauchy sequences and offered the Cauchy convergence criterion.



Article Details

References

[1] R.Antal, V.Kumar and B.Hazarika, On ∆m-statistical convergence double sequences in intuionistic fuzzy normed spaces, Proyecciones journal of mathematics 41 (3) (2022), 697–713. Google Scholar

[2] J.Connor and J.Kline, On statistical limit points and the consistency of statistical convergence, Journal of mathematical analysis and applications 197 (2) (1996), 392–399. Google Scholar

[3] O.Duman, M.K.Khan and C.Orhan, A-statistical convergence of approximating operators, Mathematical inequalities and applications 6 (2003), 689–700. Google Scholar

[4] M.Et and R.Colak, On some generalized difference difference sequence spaces, Soochow journal of mathematical 24 (4) (1995), 377–386. Google Scholar

[5] A.Esi, Statistical convergence of triple sequences in topological groups, Annals of the University of Craiova-Mathematics and Computer Science Series 40 (1) (2013), 29–33. Google Scholar

[6] A.Esi and E.Savas, On Lacunary Statistically Convergent Triple Sequences in Probabilistic Normed Space, Applied mathematics and information sciences 5 (2015), 2529–2535. Google Scholar

[7] A.Esi, Generalized difference sequence spaces defined by Orlicz functions, General Mathematics 17 (2) (2009), 53–66. Google Scholar

[8] A.Esi, Strongly generalized difference [V λ , ∆m , p]-summable sequence spaces defined by a sequence of moduli, Nihonkai Mathematical Journal 20 (2) (2009), 99–108. Google Scholar

[9] A.Esi and K.Ozdemir, Generalized ∆m-statistical convergence in Probabilistic Normed Space, Journal of Computational Analysis and Applications 13 (5) (2011), 923–932. Google Scholar

[10] A.Esi and B.C.Tripathy, Generalized Strongly difference convergent sequences associated with multiplier sequences, Mathematica Slovaca 57 (4) (2007), 339–348. Google Scholar

[11] H.Fast, Sur la convergence statistique, Colloquium Mathematicum 2 (1951), 241–244. Google Scholar

[12] J.A.Fridy and M.K.Khan, Tauberian theorems via statistical convergence, Journal of mathematical analysis and applications 228 (1) (1998), 73–95. Google Scholar

[13] J.A.Fridy and C.Orhan, Lacunary statistical summability, Journal of mathematical analysis and applications 173 (2) (1993), 497–504. Google Scholar

[14] T.Jalal and I.A.Malik, I-convergent triple sequence spaces over n-normed space, Asia pacific journal of mathematics 5 (2) (2018), 233–242. Google Scholar

[15] T.Jalal and I.A.Malik, Some new triple sequence spaces over n-normed space, Proyecciones (Antofagasta) 37 (3) (2018), 547–564. Google Scholar

[16] T.Jalal and I.A.Malik, I-Convergence of triple difference sequence spaces over n-normed space, Tbilisi mathematical journal 11 (4) (2018), 93–102 Google Scholar

[17] T.Jalal and I.A.Malik, Topological and Algebraic Properties of Triple n-normed Spaces, Proceedings of the fifth international conference on mathematics and computing, Springer Singapore (2021),187–196. Google Scholar

[18] V.A.Khan, M.I.Idrisi and M.Ahmad, On I-convergent triple sequence spaces defined by a compact operator and an Orlicz function, TWMS Journal of Applied and Engineering Mathematics 2 (4) (2021), 1012–1022. Google Scholar

[19] V.A.Khan, M.I.Idrisi and U.Tuba, On ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator, Proyecciones (Antofagasta) 40 (5) (2021), 1227–1247. Google Scholar

[20] H.Kizmaz, On certain sequence vspaces, Canadian mathematical bulletian 24 (2) (1981), 169– 176. Google Scholar

[21] M.Mursaleen and S.A.Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, solitons and fractals 41 (5) (2009), 2414–2421. Google Scholar

[22] R.Saadati and J.H.Park, On the intuitionistic fuzzy topological spaces, Chaos, solitons and frac- tals 27 (2) (2006), 331–344. Google Scholar

[23] A.Sahiner, M.Gurdal and F.K.Duden, Triple sequences and their statistical convergence, Tu ̈rkiye klinikleri psikiyatri dergisi 8 (2) (2007), 49–55. https://search.trdizin.gov.tr/tr/yayin/detay/74124/triple-sequences-and-their-statistical-convergence Google Scholar

[24] B.Schweizer and A.Sklar, Statistical Metric Spaces, Pacific journal of mathematics 10 (1) (1960), 313–334. Google Scholar

[25] M.Sen and P.Debnath, Lacunary statistical convergence in intuitionistic fuzzy n-normed spaces, Math. Comput. Model 54 (2011), 2978–2985. Google Scholar

[26] B.C.Tripathy, A.Esi and B.Tripathy, On a new type of generalized difference cesaro sequence spaces, Soochow Journal of Mathematics 31 (3) (2005), 333–340. Google Scholar

[27] B.C.Tripathy and A.Esi, A new type difference sequence spaces, International Journal of Science and Technology 1 (1) (2006), 11–14. Google Scholar

[28] L.A.Zadeh, Fuzzy sets, Information and control 8 (3) (1965), 338–353. Google Scholar