\(\mathcal{I}\)-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCES IN MEASURE

Amit Halder     (Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India)
Shyamal Debnath     (Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India)

Abstract


The main aim of this paper is to present and explore some of properties of the concept of \(\mathcal{I}\)-statistical convergence in measure of complex uncertain sequences. Furthermore, we introduce the concept of \(\mathcal{I}\)-statistical Cauchy sequence in measure and study the relationships between different types of convergencies. We observe that, in complex uncertain space, every \(\mathcal{I}\)-statistically convergent sequence in measure is \(\mathcal{I}\)-statistically Cauchy sequence in measure, but the converse is not necessarily true.

Keywords


\(\mathcal{I}\)-convergence, \(\mathcal{I}\)-statistical convergence, Uncertainty theory, Complex uncertain variable

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References


  1. Chen X., Ning Y., Wang X. Convergence of complex uncertain sequences. J. Intell. Fuzzy Syst., 2016. Vol. 30, No. 6. P. 3357–3366. DOI: 10.3233/IFS-152083
  2. Debnath S., Das B. Statistical convergence of order α for complex uncertain sequences. J. Uncertain Syst., 2021. Vol. 14, No. 2. Art. no. 2150012. DOI: 10.1142/S1752890921500124
  3. Debnath S., Das B. On λ-statistical convergence of order α for complex uncertain sequences. Int. J. Gen. Syst., 2022. Vol. 52, No. 2. P. 191–202. DOI: 10.1080/03081079.2022.2132490
  4. Debnath S., Das B. On rough statistical convergence of complex uncertain sequences. New Math. Nat. Comput., 2023. Vol. 19, No. 1. P. 1–17. DOI: 10.1142/S1793005722500454
  5. Debnath S., Debnath J. On \(\mathcal{I}\)-statistically convergent sequence spaces defined by sequence of Orlicz functions using matrix transformation. Proyecciones J. Math., 2014. Vol. 33, No. 3. P. 277–285. DOI: 10.4067/S0716-09172014000300004
  6. Debnath S., Rakshit D. On \(\mathcal{I}\)-statistical convergence. Iranian J. Math. Sci. Inform., 2018. Vol. 13, No. 2. P. 101–109. DOI: 10.7508/ijmsi.2018.13.009
  7. Esi A. Debnath S., Saha S. Asymptotically double \(\lambda_{2}\)-statistically equivalent sequences of interval numbers. Mathematica, 2020. Vol. 62(85), No. 1. P. 39–46. DOI: 10.24193/mathcluj.2020.1.05
  8. Fast H. Sur la convergence statistique. Colloq. Math., 1951. Vol. 2, No. 3–4. P. 241–244. (in French)
  9. Fridy J.A. On statistically convergence. Analysis, 1985. Vol. 5, No. 4. P. 301–313. DOI: 10.1524/anly.1985.5.4.301
  10. Kişi Ö. S \(S_{\lambda}(\mathcal{I})\)-convergence of complex uncertain sequences. Mat. Stud., 2019. Vol. 51, No. 2. P. 183–194.
  11. Kostyrko P., Wilczyński W., Salát T. \(\mathcal{I}\)-convergence. Real Anal. Exchange, 2000/2001. Vol. 26, No. 2. P. 669–686.
  12. Liu B. Uncertainty Theory, 4th ed. Berlin, Heidelberg: Springer-Verlag, 2015. 487 p. DOI: 10.1007/978-3-662-44354-5
  13. Mursaleen M., Debnath S., Rakshit D. \(\mathcal{I}\)-statistical limit superior and I-statistical limit inferior. Filomat, 2017. Vol. 31, No. 7. P. 2103–2108. DOI: 10.2298/FIL1707103M
  14. Nath P.K., Tripathy B.C. Convergent complex uncertain sequences defined by Orlicz function. Ann. Univ. Craiova-Math. Comput. Sci. Ser., 2019. Vol. 46, No. 1. P. 139–149. 
  15. Peng Z. Complex Uncertain Variable. PhD, Tsinghua University, 2012.
  16. Roy S., Tripathy B.C., Saha S. Some results on \(p\)-distance and sequence of complex uncertain variables. Commun. Korean. Math. Soc., 2020. Vol. 35, No. 3. P. 907–916. DOI: 10.4134/CKMS.c200026
  17. Saha S., Tripathy B. C., Roy S. On almost convergence of complex uncertain sequences. New Math. Nat. Comput., 2016. Vol. 16, No. 03. P. 573–580. DOI: 10.1142/S1793005720500349
  18. Savas E., Das P. A generalized statistical convergence via ideals. App. Math. Lett., 2011. Vol. 24, No. 6. P. 826–830. DOI: 10.1016/j.aml.2010.12.022
  19. Savas E., Das P. On \(\mathcal{I}\)-statistically pre-Cauchy sequences. Taiwanese J. Math., 2014. Vol. 18, No. 1. P. 115–126. DOI: 10.11650/tjm.18.2014.3157
  20. Savas E., Debnath S., Rakshit D. On \(\mathcal{I}\)-statistically rough convergence. Publ. Inst. Math., 2019. Vol. 105, No. 119. P. 145–150. DOI: 10.2298/PIM1919145S
  21. Steinhaus H. Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math., 1951. Vol. 2, No. 1. P. 73–74. (in French)
  22. Tripathy B.C., Nath P.K. Statistical convergence of complex uncertain sequences. New Math. Nat. Comput., 2017. Vol. 13, No. 3. P. 359–374. DOI: 10.1142/S1793005717500090
  23. You C., Yan L. Relationships among convergence concepts of uncertain sequences. Comput. Model. New Technol., 2016. Vol. 20, No. 3. P. 12–16.
  24. Wu J., Xia Y. Relationships among convergence concepts of uncertain sequences. Inform. Sci., 2012. Vol. 198. P. 177–185. DOI: 10.1016/j.ins.2012.02.048




DOI: http://dx.doi.org/10.15826/umj.2024.2.007

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