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Open Access Research Article

On Δm (J) summability in neutrosophic-n-normed linear spaces 

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pp. 1887–1893Vol. 27Issue 8December 2024DOI: 10.47974/JIM-2054XML
Received:
10 Jul 2024
Published Online:
16 Dec 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-2054
Pages:
1887–1893

Abstract

For the difference operator ∆m and the admissible ideal J ⊆ P(N), we aim in present work to introduce ∆m (J*N)-summability and ∆m (J*N)-summability in neutrosophic-n-normed linear spaces (briefly called N-n-NLS). We explore some basic properties of ∆m (J*N)-summability and ∆m (J*N)-summability and find conditions on J for which the two summability methods coincide. Finally, we define ∆m (JN)-Cauchy sequences in N-n-NLS and obtain the Cauchy convergence criteria.

Keywords

Subject Classifications

40A3540A05

References

[1] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96 (1986).
[2] J. Connor, “The statistical and strong p-Cesaro convergence of sequences,” Analysis, vol. 8, no. 1–2, pp. 47–64 (1988).
[3] K. Demirci, “I-limit superior and limit inferior,” Math. Commun., vol. 6, no. 2, pp. 165–172 (2001).
[4] K. Dems, “On I Cauchy sequences,” Real Anal. Exch., vol. 30, no. 1 (2004).
[5] M. Et and R. Colak, “On some generalized difference sequence spaces,” Soochow J. Math., vol. 21, no. 4, pp. 377–386 (1995).
[6] H. Fast, “Sur la convergence statistique,” Colloq. Math., vol. 2, no. 3–4, pp. 241–244 (1951).
[7] J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–314 (1985).
[8] S. Gähler, “Linear 2-normierte Räume,” Math. Nachr., vol. 28, pp. 1–43 (1965).
[9] H. Gunawan and M. Mashadi, “On n-normed spaces,” Int. J. Math. Math. Sci., vol. 27, no. 10, pp. 631–639 (2001).
[10] N. Harnpornchai and W. Wonggattaleekam, “An application of neutrosophic set to relative importance assignment in AHP,” Mathematics, vol. 9, no. 20, p. 2636 (2021).
[11] V. A. Khan, M. D. Khan, and M. Ahmad, “Some new type of lacunary statistically convergent sequences in neutrosophic normed space,” Neutrosophic Sets Syst., vol. 42 (2021).
[12] M. Kirişci and N. Şimşek, “Neutrosophic normed spaces and statistical convergence,” J. Anal., vol. 28, pp. 1059–1073 (2020).
[13] K. Kumar and V. Kumar, “On the I and I* convergence of sequences in fuzzy normed spaces,” Adv. Fuzzy Sets, vol. 3, pp. 341–365 (2008).
[14] V. Kumar and M. Mursaleen, “On (λ, μ)-statistical convergence of double sequences on intuitionistic fuzzy normed spaces,” Filomat, vol. 25, no. 2, pp. 109–120 (2011).
[15] V. Kumar and B. Lafuerza-Guillén, “On ideal convergence of double sequences in probabilistic normed spaces,” Acta Math. Sin., English Ser., vol. 28, pp. 1689–1700 (2012).
[16] D. Koundal, S. Gupta, and S. Singh, “Applications of neutrosophic sets in medical image denoising and segmentation,” Infinite Study (2016).
[17] P. Kostyrko, M. Macaj, T. Šalát, and M. Sleziak, “I-convergence and extremal I-limit points,” Math. Slovaca, vol. 55, no. 4, pp. 443–464 (2005).
[18] P. Kostyrko, P. Šalát, and W. Wilczyński, “I-convergence,” Real Anal. Exch., vol. 26, no. 2, pp. 669–685 (2000).
[19] V. Kumar, A. Sharma, and S. Murtaza, “On neutrosophic n-normed linear spaces,” Neutrosophic Sets Syst., vol. 61, pp. 275–288 (2023).
[20] I. J. Maddox, “Statistical convergence in a locally convex space,” Math. Proc. Cambridge Philos. Soc., vol. 104, no. 1, pp. 141–145 (1988).
[21] M. Mursaleen, “λ-statistical convergence,” Math. Slovaca, vol. 50, no. 1, pp. 111–115 (2000).
[22] P. Majumdar, “Neutrosophic sets and its applications to decision making,” in Computational Intelligence for Big Data Analysis, Springer, Cham, pp. 97–115 (2015).
[23] S. Murtaza, A. Sharma, and V. Kumar, “Neutrosophic 2-normed space and generalized summability,” Neutrosophic Sets Syst., vol. 55, no. 1, pp. 414–426 (2023).
[24] A. Nabiev, S. Pehliva, and M. Gürdal, “On I-Cauchy sequences,” Taiwanese J. Math., vol. 11, no. 2, pp. 569–576 (2007).
[25] M. Parimala, F. Smarandache, S. Jafari, and R. Udhayakumar, “On neutrosophic αψ-closed sets,” Information, vol. 9, no. 5, p. 103 (2018).
[26] M. Parimala, M. Karthik, S. Jafari, F. Smarandache, and R. Udhayakumar, “Decision-making via neutrosophic support soft topological spaces,” Symmetry, vol. 10, no. 6, p. 217 (2018).
[27] M. Parimala, M. Karthik, S. Jafari, F. Smarandache, and R. Udhayakumar, “Neutrosophic nano ideal topological structure,” Neutrosophic Sets Syst., vol. 24, pp. 70–76 (2019).
[28] I. J. Schoenberg, “The integrability of certain functions and related summability methods,” Amer. Math. Monthly, vol. 66, no. 5, pp. 361–375 (1959).
[29] F. Smarandache, “Neutrosophic set: a generalization of intuitionistic fuzzy sets,” Int. J. Pure Appl. Math., vol. 24, pp. 287–297 (2005).
[30] T. Šalát, “On statistically convergent sequences of real numbers,” Math. Slovaca, vol. 30, no. 2, pp. 139–150 (1980).
[31] A. Sharma and V. Kumar, “Some remarks on generalized summability using difference operators on neutrosophic normed spaces,” J. Ramanujan Soc. Math. Math. Sci., vol. 9, no. 2, pp. 153–164 (2022).
[32] A. Sharma, S. Murtaza, and V. Kumar, “Some remarks on ∆n(Iλ)-summability on neutrosophic normed spaces,” Int. J. Neutrosophic Sci., vol. 19, pp. 68–81 (2022).
[33] A. Sharma, V. Kumar, and I. R. Ganaie, “Some remarks on I(Sθ)-summability via neutrosophic norm,” Filomat, vol. 37, no. 20, pp. 6699–6707 (2023).
[34] B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific J. Math., vol. 10, no. 1, pp. 313–334 (1960).
[35] L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, pp. 338–353 (1965).

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