Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

CERTAIN ASPECTS OF ROUGH IDEAL STATISTICAL CONVERGENCE ON NEUTROSOPHIC NORMED SPACES

  • Reena Antal (Department of Mathematics, Chandigarh University) ;
  • Meenakshi Chawla (Department of Mathematics, Chandigarh University) ;
  • Vijay Kumar (Department of Mathematics, Chandigarh University)
  • Received : 2023.11.03
  • Accepted : 2024.02.01
  • Published : 2024.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we have presented rough ideal statistical convergence of sequence on neutrosophic normed spaces as a significant convergence criterion. As neutrosophication can handle partially dependent components, partially independent components and even independent components involved in real-world problems. By examining some properties related to rough ideal convergence in these spaces we have established some equivalent conditions on the set of ideal statistical limit points for rough ideal statistically convergent sequences.

Keywords

References

  1. R. Antal, M. Chawla, V. Kumar, Rough statistical convergence in intutionistic fuzzy normed spaces, Filomat, 35 (13) (2021), 4405-4416. https://doi.org/10.2298/FIL2113405A
  2. R. Antal, M. Chawla, V. Kumar, Rough statistical convergence in probabilistic normed spaces, Thai J. Math. 20 (4) (2023), 1707-1719.
  3. M. Arslan, E. Dundar, On rough convergence in 2-normed spaces and some properties, Filomat, 33 (16) (2019), 5077-5086. https://doi.org/10.2298/FIL1916077A
  4. S. Aytar, Rough statistical convergence, Numer. Funct. Anal. Optimiz. 29 (3-4) (2008), 291-303. https://doi.org/10.1080/01630560802001064
  5. S. Aytar, Rough statistical cluster points, Filomat, 31 (16) (2017), 5295-5304. https://doi.org/10.2298/FIL1716295A
  6. A. K. Banerjee, A. Paul, Rough I-convergence in cone metric spaces, J. Math. Comput. Sci. 12 (2022).
  7. T. Bera , N. K. Mahapatra, On neutrosophic soft linear spaces, Fuzzy Inf. Eng. 9 (3) (2017), 299-324. https://doi.org/10.1016/j.fiae.2017.09.004
  8. S. Debnath, D. Rakshit, Rough convergence in metric spaces, New Trends in Analysis and Interdisciplinary Applications (2017), 449-454. https://doi.org/10.1007/978-3-319-48812-7_57
  9. S. Debnath, N. Subramanian, Rough statistical convergence on triple sequences, Proyecciones (Antofagasta), 36 (4) (2017), 685-699. http://dx.doi.org/10.4067/S0716-09172017000400685
  10. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (3-4) (1951), 241-244.
  11. J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
  12. V. A. Khan , M. D. Khan, M. Ahmad, Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets and Systems, 42 (2021), 239-252. https://digitalrepository.unm.edu/nss_journal/vol42/iss1/15
  13. V. A. Khan , M. D. Khan, M. Ahmad, Some Results of Neutrosophic Normed Spaces via Fibonacci Matrix, Infinite Study, 2021.
  14. M. Kirisci, N. Simsek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241-248. https://doi.org/10.1007/s40096-020-00335-8
  15. M. Kirisci, N. Simsek, Neutrosophic normed spaces and statistical convergence, J. Anal., 28(4) (2020), 1059-1073. https://doi.org/10.1007/s41478-020-00234-0
  16. O. Kisi, Convergence methods for double sequences and applications in neutrosophic normed spaces, Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences, 2021, 137-154, CRC Press.
  17. O. Kisi, Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41 (2) (2021), 2581-2590. https://doi.org/10.3233/JIFS-201568
  18. O. Kisi, E. Dundar, Rough I2-lacunary statistical convergence of double sequences, J. Inequal Appl., 1 (2018), 1-16. https://doi.org/10.1186/s13660-018-1831-7
  19. Kisi O., Gurdal V. On triple difference sequences of real numbers in neutrosophic normed spaces, Commun. Adv. Math. Sci. 5 (1) (2022), 35-45. https://doi.org/10.33434/cams.1025928
  20. P. Kostyrko, T. Sal'at, W. Wilczynski, I-convergence, Real analysis exchange, 2000, 669-685.
  21. P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat., 27 (1-2) (2016), 141-148. https://doi.org/10.1007/s13370-015-0332-9
  22. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimiz., 22 (1-2) (2001), 199-222. https://doi.org/10.1081/NFA-100103794
  23. F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (3) (2005), 287.
  24. H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets. Infinite study, 2010.
  25. J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst. 26 (5) (2014), 2459-2466. https://doi.org/10.3233/IFS-130916