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Statistical Fibonacci convergence of complex uncertain variables

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Abstract

This paper presents several statistical convergence concepts of complex uncertain sequences based on a regular matrix of Fibonacci numbers: statistical Fibonacci convergence almost surely, statistical Fibonacci convergence in measure, statistical Fibonacci convergence in mean and statistical Fibonacci convergence uniformly almost surely. Furthermore, the interrelations between them are studied and depicted in the form of a diagram.

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References

  1. Basarir, M., Basar, F., Kara, E.E.: On the spaces of Fibonacci difference null and convergent sequences, arXiv preprint arXiv:1309.0150, (2013)

  2. Chen, X., Ning, Y., Wang, X.: Convergence of complex uncertain sequences. J. Intell. Fuzzy Syst. 30(6), 3357–3366 (2016)

    Article  MATH  Google Scholar 

  3. Debnath, S., Saha, S.: Some newly defined sequence spaces using regular matrix of fibonacci numbers. AKU-J. Sci. Eng. 14(1), 1–3 (2014)

    Article  Google Scholar 

  4. Fast, H.: Sur la convergence statistique. Colloq math. 2(3–4), 241–244 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  5. Koshy, T.: Fibonacci and Lucas numbers with applications. Wiley (2001)

    Book  MATH  Google Scholar 

  6. Kara, E.E., Basarir, M.: An application of Fibonacci numbers into infinite Toeplitz matrices. Caspian J. Math. Sci. 1(1), 43–47 (2012)

    MATH  Google Scholar 

  7. Kalman, D., Mena, R.: The Fibonacci numbers-exposed. Math. Mag. 76(3), 167–181 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Liu, B.: Uncertainty Theory, 5th edn. Springer-Verlag, Berlin (2016)

    Google Scholar 

  9. Nath, P.K., Tripathy, B.C.: Statistical convergence of complex uncertain sequences defined by Orlicz function. Proyecciones J. Math. 39(2), 301–315 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  10. Peng, Z.X.: Complex uncertain variable. Doctoral Dissertation. Tsinghua University (2012)

  11. Roy, S., Saha, S., Tripathy, B.C.: Some Results on \(p-\)distance and sequence of complex uncertain variables. Commun. Korean Math. Soc. 35(3), 907–916 (2020)

    MathSciNet  MATH  Google Scholar 

  12. Schoenberg, I.J.: The integrability of certain functions and related summability methods. Am. Math. Mon. 66(5), 361–775 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  13. Saha, S., Tripathy, B.C., Roy, S.: On Almost Convergent of Complex Uncertain Sequences. New Math. Nat. Comput. 16(3), 573–580 (2020)

  14. Saha, S., Tripathy, B.C., Roy, S.: Matrix Map Between Complex Uncertain Sequences. Ann. Univ. Craiova-Math. Comput. Sci. Ser. 48(1), 10–17 (2021)

  15. Tripathy, B.C., Nath, P.K.: Statistical convergence of complex uncertain sequences. New Math. Nat. Comput. 13(3), 359–374 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vajda, S.: Fibonacci and Lucas Numbers, and Golden Section: Theory and Applications. Ellis Horword, Chichester (1989)

    MATH  Google Scholar 

  17. You, C.L.: On the convergence of uncertain sequences. Math. Comput. Model. 49(3–4), 482–487 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. You, C., Yan, L.: Relationships among convergence concepts of uncertain sequences. Comput. Model. New Technol. 20(3), 12–16 (2016)

    Google Scholar 

  19. You, C., Yan, L.: The p-distance of uncertain variables. J. Intell. Fuzzy Syst. 32(1), 999–1006 (2017)

    Article  MATH  Google Scholar 

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Correspondence to Binod Chandra Tripathy.

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Saha, S., Tripathy, B.C. Statistical Fibonacci convergence of complex uncertain variables. Afr. Mat. 34, 76 (2023). https://doi.org/10.1007/s13370-023-01119-8

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