Triple Lacunary $\Delta $-Statistical Convergence in Neutrosophic Normed Spaces
Triple Lacunary $\Delta $-Statistical Convergence in Neutrosophic Normed Spaces
The aim of this article is to investigate triple lacunary $\Delta $ -statistically convergent and triple lacunary $\Delta $-statistically Cauchy sequences in a neutrosophic normed space (NNS). Also, we present their feature utilizing triple lacunary density and derive the relationship between these notions.
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- [1] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24(3) (2005), 287–297.
- [2] F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 1998.
- [3] M. Kirisci, N. S¸ims¸ek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241–248.
- [4] M. Kirisci, N. S¸ims¸ek, Neutrosophic normed spaces and statistical convergence, J. Anal., 28 (2020), 1059–1073.
- [5] M. Kirisci, N. S¸ims¸ek, M. Akyi˘git, Fixed point results for a new metric space, Math. Methods Appl. Sci., 44(9) (2020), 7416–7422.
- [6] O¨ . Kis¸i, Lacunary statistical convergence of sequences in neutrosophic normed spaces, 4th International Conference on Mathematics: An Istanbul
Meeting for World Mathematicians, Istanbul, 2020, 345–354.
- [7] O¨ . Kis¸i, Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2) (2021), 2581–2590.
- [8] V.A. Khan, M.D. Khan, M. Ahmad, Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets
Syst., 42 (2021), 239–252.
- [9] A. Zygmund, Trigonometric series, Cambridge University Press, Cambridge, UK, 1979.
- [10] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
- [11] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
- [12] A.A. Nabiev, E. Savas¸, M. G¨urdal, Statistically localized sequences in metric spaces,J. Appl. Anal. Comput., 9(2) (2019), 739–746.
- [13] E. Savas¸, M. G¨urdal, Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Systems, 27(4) (2014),
2067–2075.
- [14] M. Mursaleen, O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231.
- [15] B. Altay, F. Bas¸ar, Some new spaces of double sequences, J. Math. Anal. Appl., 309 (1) (2005), 70–90.
- [16] M. G¨urdal, A. S¸ ahiner, Extremal I-limit points of double sequences, Appl. Math. E-Notes, 8 (2008), 131–137.
- [17] A. S¸ ahiner, M. G¨urdal, F.K. D¨uden, Triple sequences and their statistical convergence, Selc¸uk J. Appl. Math., 8(2) (2007), 49–55.
- [18] A. Esi, E. Savas¸, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9(5) (2015), 2529–2534.
- [19] M.B. Huban, M. G¨urdal, Wijsman lacunary invariant statistical convergence for triple sequences via Orlicz function, J. Classical Anal., 17(2) (2021),
119–128.
- [20] A. Esi, Statistical convergence of triple sequences in topological groups, Annals Univ. Craiova. Math. Comput. Sci. Ser., 10(1) (2013), 29–33.
- [21] B.C. Tripathy, R. Goswami, On triple difference sequences of real numbers in propobabilistic normed space, Proyecciones J. Math., 33(2) (2014),
157–174.
- [22] J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pac. J. Math., 160(1) (1993), 43–51.
- [23] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Syst., 99(3) (1998), 353–355.
- [24] U. Yamanci , M. Gurdal, On lacunary ideal convergence in random n-normed space, J. Math., 2013, Article ID 868457, 8 pages.
- [25] H. Kızmaz,On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169–176.
- [26] M. Bas¸arır, On the statistical convergence of sequences, Fırat Univ. Turk. J. Sci. Technol., 2 (1995), 1–6.
- [27] T. Bilgin, Lacunary strongly D-convergent sequences of fuzzy numbers, Inform. Sci., 160 (2004), 201–206.
- [28] B. Hazarika, Lacunary generalized difference statistical convergence in random 2-normed spaces, Proyecciones, 31 (2012), 373–390.
- [29] R. C¸ olak, H. Altınok, M. Et, Generalized difference sequences of fuzzy numbers, Chaos Solitons Fractals, 40(3) (2009), 1106–1117.
- [30] Y. Altın, M. Bas¸arır, M. Et, On some generalized difference sequences of fuzzy numbers, Kuwait J. Sci., 34(1A) (2007), 1–14.
- [31] S. Altunda˘g, E. Kamber, Lacunary D-statistical convergence in intuitionistic fuzzy n-normed space, J. Inequal. Appl., 2014(40) (2014), 1–12.
- [32] B. Hazarika, A. Alotaibi, S.A. Mohiudine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24(9)
(2020), 6613–6622.
- [33] F. Bas¸ar, Summability theory and its applications, Bentham Science Publishers, ˙Istanbul, 2012.
- [34] M. Mursaleen, F. Bas¸ar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its
Applications, Boca Raton London New York, 2020.
- [35] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA 28(12) (1942), 535–537.