Have a personal or library account? Click to login
Neutrosophic Fuzzy Tribonacci ℐ-Lacunary Statistical Convergent Sequence Spaces Cover

Neutrosophic Fuzzy Tribonacci ℐ-Lacunary Statistical Convergent Sequence Spaces

Open Access
|Oct 2024

References

  1. ATANASSOV, K. T.: Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), no. 1, 87–96.
  2. DEBNATH, P.: Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl. 63 (2012), no. 3, 708–715.
  3. FAST, H.: Sur la convergence statistique, Colloq. Math. 2 (1952), 241–244.
  4. FEINBERG, M.: Fibonacci-tribonacci, Fibonacci Quart. 1 (1963), 71–74.
  5. FRIDY, J. A.—ORHAN, C.: Lacunary statistical convergence, Pacific J. Math. 160 (1993), no. 1, 43–51.
  6. GEORGE, A.—VEERAMANI, P.: On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems. 90 (1997), no. 3, 365–368.
  7. GÜRDAL, M.—ŞAHINER, A.: Extremal ℐ-limit points of double sequences, Appl. Math. E-Notes 8 (2008), 131–137.
  8. KADAK, U.—MOHIUDDINE, S. A.: Generalized statistically almost convergence based on the difference operator which includes the (p,q)-Gamma function and related approximation theorems,Results Math. 73 (2018), no. 1, Paper no. 9, 31 pp.
  9. KALEVA, O.—SEIKKALA, S.: On fuzzy metric spaces, Fuzzy Sets and Systems. 12 (1984), no. 3, 215–229.
  10. KARAKUS, S.—DEMIRCI, K.—DUMAN, O.: Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals 35 (2008), no. 4, 215–229.
  11. KHAN, V. A.—AHMAD, M.—FATIMA, H.—KHAN, F. M.: On some results in intuitionistic fuzzy ideal convergence double sequence spaces, Adv. Difference Equ. 2019 (2019), no. 1, Paper No. 375, 10 pp.
  12. KHAN, V. A.—FATIMA, H.—ALTAF, H.—LOHANI, Q. M. D.—SRIVASTAVA, H. M.: Intuitionistic fuzzy I-convergent sequence spaces defined by compact operator, Cogent Math. 3 (2016), no. 1, Article ID: 1267904.
  13. KHAN, V. A.—KARA, E.—ALTAF, H.—KHAN, N.—AHMAD, M.: Intuitionistic fuzzy ℐ-convergent Fibonacci difference sequence spaces, J. Inequal. Appl. 2019 (2019), Article no. 202, 7 pp.
  14. KHAN, V. A.—RAHAMAN, S. K. A.: Intuitionistic fuzzy tribonacci convergent sequence spaces, Math. Slovaca 72 (2022), no. 3, 693–708.
  15. KIRIŞCI, M.—ŞIMŞEK, N.: Neutrosophic metric spaces, Math. Sci. 14 (2022), no. 3, 241–248.
  16. KIRIŞCI M.—ŞIMŞEK, N.: Neutrosophic normed spaces and statistical convergence, J. Anal. 28 (2020), no. 4, 1059–1073.
  17. KIŞI,Ö.: Ideal convergence of sequences in neutrosophic normed spaces,J.Intell. Fuzzy Systems 41 (2021), no. 2, 2581–2590.
  18. KOSTYRKO, P.—˘SALÁT, T.—WILCZYNSSKI, W.: ℐ-convergence, Real Anal. Exchange 26 (2000), no. 2, 669–686.
  19. KRAMOSIL, I.—MICHALEK, J.: Fuzzy metric and statistical metric spaces,Kybernetika 11 (1975), no. 5, 336–344.
  20. LAEL, F.—NOUROUZI, K.: Some results on the IF-normed spaces, Chaos Solitons Fractals 37 (2008), no. 3, 931–939.
  21. MENGER, K.: Statistical metrics, Proc. Nat. Acad. Sci. U.S.A 28 (1942), 535–537.
  22. MOHIUDDINE, S. A.—ASIRI, A.—HAZARIKA, H.: Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int.J.Gen. Syst. 48 (2019), no. 5, 492–506.
  23. MOHIUDDINE, S. A.—DANISH LOHANI, Q. M.: On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals 42 (2009), no. 3, 1731–1737.
  24. MURSALEEN, M.—MOHIUDDINE, S. A.: On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math. 233 (2009), no. 2, 142–149.
  25. MURSALEEN, M.—MOHIUDDINE, S. A.—EDELY, O. H. H.: On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl. 59 (2010), no. 2, 603–611.
  26. NABIEV, A. A.—PEHLIVAN, S.—GÜRDAL, M.: On I−Cauchy sequences,Taiwanese J. Math. 11 (2007), no. 2, 569–566.
  27. PARK,J.H.: Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), no. 5, 1039–1046.
  28. RATH, D.—TRIPATHY, B. C.: Matrix maps on sequence spaces associated with sets of integers, Indian J. Pure Appl. Math. 27 (1996), 197–206.
  29. SAVAŞ, E.—DAS, P.: A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), no. 6, 826–830.
  30. SAVAŞ, E.—GÜRDAL, M.: Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems 27 (2014), no. 4, 1621–1629.
  31. SAVAŞ, E.—GÜRDAL, M.: A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia 41 (2015), nno. 4, 289–294.
  32. SAVAŞ, E.—GÜRDAL, M.: Ideal convergent function sequences in random 2-normed spaces, Filomat 30 (2016), no. 3, 557–567.
  33. SMARANDACHE, F.: Neutrosophy. Neutrosophic Probability, Set, and Logic. Ed. of ProQuest Information & Learning, Ann Arbor, Michigan, USA, 1998.
  34. SMARANDACHE, F.: Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24 (2005), no. 3, 287–297.
  35. KHAN, V. A.—ARSHAD, M.: On some properties of Nörlund ideal convergence of sequence in neutrosophic normed spaces, Ital. J. Pure Appl. Math. 40 (2023) 1–8.
  36. KHAN, V. A.—ARSHAD, M.—KHAN, M. D.: Some results of neutrosophic normed space VIA Tribonacci convergent sequence spaces, J. Inequal. Appl. 2022, paper no. 42, 27 pp.
  37. KHAN, V. A.— ARSHAD, M.—–ALAM, M.: Riesz deal convergence in neutrosophic normed spaces. J. Intell. Fuzzy Systems. 42 (2023). no. 4, 1–10.
  38. TAN, B.—WEN,Z.Y.: Some properties of the tribonacci sequence, European J. Combin. 28 (2007), no. 6, 1703–1719.
  39. TRIPATHY, B. C.—HAZARIKA, B.—CHOUDHARY, B.: Lacunary ℐ−convergent sequences, Kyungpook Math. J. 52 (2012), no. 4, 473–482.
  40. TRIPATHY, B. C.—SEN, M.: On fuzzy ℐ−convergent difference sequence spaces, J. Intell. Fuzzy Syst. 25 (2013), no. 3, 643–647.
  41. WILANSKY, A.: Summability through functional analysis. North-Holland Mathematics Stud. Vol. 85. Notas Mat. Vol. 91. [Mathematical Notes] North-Holland Publishing Co., Amsterdam-New York-Oxford, 1984.
  42. YAYING, T.—HAZARIKA, B.: On sequence spaces defined by the domain of a regular tribonacci matrix, Math. Slovaca 70 (2020), no. 3, 697–706.
  43. ZADEH, L. A.: Fuzzy sets,Inf.Control 8 (1965), no. 3, 338–353.
DOI: https://doi.org/10.2478/tmmp-2024-0015 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 147 - 174
Submitted on: Feb 18, 2024
Accepted on: Jun 18, 2024
Published on: Oct 20, 2024
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Vakeel A. Khan, Ömer Kişi, Chiranjib Choudhury, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.