Applications of Strongly Deferred Weighted Convergence in the Environment of Uncertainty

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-181
Published: Oct 15, 2024
Cite as:
Sonali Sharma, Kuldip Raj, Sunil K. Sharma, Thwiba A. Khalid, Arafa O. Mustafa, Mustafa M. Mohammed, Runda A. A. Bashir, Awad A. Bakery, Applications of Strongly Deferred Weighted Convergence in the Environment of Uncertainty, Int. J. Anal. Appl., 22 (2024), 181.

Main Article Content

Sonali Sharma, Kuldip Raj, Sunil K. Sharma, Thwiba A. Khalid, Arafa O. Mustafa, Mustafa M. Mohammed, Runda A. A. Bashir, Awad A. Bakery

Abstract

In the context of uncertainty theory, we present strongly deferred weighted convergence of complex uncertain sequences. Also, we introduce strongly deferred weighted convergence of complex uncertain sequences in all five aspects of uncertainty, that is through almost surely, mean, measure, distribution and uniformly almost surely. Further, with the aid of interesting examples and diagram we investigate some interrelationships among these complex uncertain sequences.

Article Details

References

  1. X. Chen, American Option Pricing Formula for Uncertain Financial Market, Int. J. Oper. Res. 8 (2011), 27–32.
  2. X. Chen, Y. Ning, X. Wang, Convergence of Complex Uncertain Sequences, J. Intell. Fuzzy Syst. 30 (2016), 3357–3366. https://doi.org/10.3233/ifs-152083.
  3. D. Datta, B.C. Tripathy, Convergence of Complex Uncertain Double Sequences, New Math. Nat. Comp. 16 (2020), 447–459. https://doi.org/10.1142/s1793005720500271.
  4. B. Das, B.C. Tripathy, P. Debnath, J. Nath, B. Bhattacharya, Almost Convergence of Complex Uncertain Triple Sequences, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 91 (2020), 245–256. https://doi.org/10.1007/s40010-020-00721-w.
  5. B. Das, B. Tripathy Chandra, P. Debnath, B. Bhattacharya, Almost Convergence of Complex Uncertain Double Sequences, Filomat 35 (2021), 61–78. https://doi.org/10.2298/fil2101061d.
  6. H. Guo, C. Xu, A Necessary and Sufficient Condition of Convergence in Mean Square for Uncertain Sequences, Int. Interdiscip. J. Sch. Res. 16 (2013), 1091–1096.
  7. B. Liu, Uncertain Set Theory and Uncertain Inference Rule With Application to Uncertain Control, J. Uncertain Syst. 4 (2010), 83–98.
  8. B. Liu, Uncertainty Theory, Springer, Berlin, 2007. https://doi.org/10.1007/978-3-540-73165-8.
  9. B. Liu, Uncertainty Theory, in: Uncertainty Theory, Springer, Berlin, 2010: pp. 1–79. https://doi.org/10.1007/978-3-642-13959-8_1.
  10. B. Liu, Why is There a Need for Uncertainty Theory?, J. Uncertain Syst. 6 (2012), 3–10.
  11. B. Liu, Some Research Problems in Uncertain Theory, J. Uncertain Syst. 3 (2009), 3–10.
  12. B. Liu, Uncertain Risk Analysis and Uncertain Stability Analysis, J. Uncertain Syst. 4 (2010), 163–170.
  13. B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer, Berlin, 2010. https://doi.org/10.1007/978-3-642-13959-8.
  14. I.J. Maddox, Spaces of Strongly Summable Sequences, Q. J. Math. 18 (1967), 345–355. https://doi.org/10.1093/qmath/18.1.345.
  15. Mursaleen, O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231. https://doi.org/10.1016/j.jmaa.2003.08.004.
  16. P.K. Nath, B.C. Tripathy, Convergent Complex Uncertain Sequences Defined by Orlicz Function, Ann. Univ. Craiova - Math. Comp. Sci. Ser. 46 (2019), 139–149.
  17. J. Nath, B.C. Tripathy, P. Debnath, B. Bhattacharya, Strongly Almost Convergence in Sequences of Complex Uncertain Variables, Comm. Stat. - Theory Meth. 52 (2021), 714–729. https://doi.org/10.1080/03610926.2021.1921802.
  18. K. Ömer, H.K. Ünal, Lacunary Statistical Convergence of Complex Uncertain Sequence, Sigma J. Eng. Nat. Sci. 10 (2019), 277–286.
  19. K. Ömer, Sλ(I)-Convergence of Complex Uncertain Sequence, Mat. Stud. 51 (2019), 183–194.
  20. Z. Peng, Complex Uncertain Variables, Doctoral Dissertation, Tsinghua University, 2012.
  21. K. Raj, S. Sharma, M. Mursaleen, Almost λ-Statistical Convergence of Complex Uncertain Sequences, Int. J. Unc. Fuzz. Knowl. Based Syst. 30 (2022), 795–811. https://doi.org/10.1142/s0218488522500234.
  22. K. Saini, K. Raj, Applications of Statistical Convergence in Complex Uncertain Sequences via Deferred Riesz Mean, Int. J. Unc. Fuzz. Knowl. Based Syst. 29 (2021), 337–351. https://doi.org/10.1142/s021848852150015x.
  23. H. M. Srivastava, B. B. Jena and S. K. Paikray, Statistical Probability Convergence via the Deferred Nörlund Mean and Its Applications to Approximation Theorems, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114 (2020), 144. https://doi.org/10.1007/s13398-020-00875-7.
  24. S. Saha, B.C. Tripathy, S. Roy, On Almost Convergent of Complex Uncertain Sequences, New Math. Nat. Comp. 16 (2020), 573–580. https://doi.org/10.1142/s1793005720500349.
  25. B.C. Tripathy, P.J. Dowari, Nörlund and Riesz Mean of Sequences of Complex Uncertain Variables, Filomat 32 (2018), 2875–2881. https://doi.org/10.2298/fil1808875t.
  26. B.C. Tripathy, P.K. Nath, Statistical Convergence of Complex Uncertain Sequences, New Math. Nat. Comp. 13 (2017), 359–374. https://doi.org/10.1142/s1793005717500090.
  27. C. You, On the Convergence of Uncertain Sequences, Math. Comp. Model. 49 (2009), 482–487. https://doi.org/10.1016/j.mcm.2008.07.007.