SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 3

Some results on $I_2$-deferred statistically convergent double sequences in fuzzy normed spaces

Ömer Kişi(BARTIN UNIVERSITY)0000-0001-6844-3092
Rümeysa Akbıyık(BARTIN UNIVERSITY)0009-0004-8751-0325
Mehmet Gürdal(SULEYMAN DEMIREL UNIVERSITY)0000-0003-0866-1869
Pages
—
Publication Date
2024-09-27
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We further define $I_2$-deferred statistical limit points and $I_2$-deferred statistical cluster points of a sequence within FNS and explore the relationships among these concepts.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The primary objective of this study is to introduce the concepts of $I_2$-deferred Cesàro summability and $I_2-$ deferred statistical convergence for double sequences in fuzzy normed spaces (FNS).
📊
Key Findings & Data:Furthermore, the aim is to explore the connections between these concepts and subsequently establish several theorems pertaining to the notion of $I_2$-deferred statistical convergence in FNS for double sequences.
💡
Conclusion & Impact:We further define $I_2$-deferred statistical limit points and $I_2$-deferred statistical cluster points of a sequence within FNS and explore the relationships among these concepts.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy normed spaces · deferred statistical convergence · Cesàro summability

Abstract

The primary objective of this study is to introduce the concepts of $I_2$-deferred Cesàro summability and $I_2-$ deferred statistical convergence for double sequences in fuzzy normed spaces (FNS). Furthermore, the aim is to explore the connections between these concepts and subsequently establish several theorems pertaining to the notion of $I_2$-deferred statistical convergence in FNS for double sequences. We further define $I_2$-deferred statistical limit points and $I_2$-deferred statistical cluster points of a sequence within FNS and explore the relationships among these concepts.

🔖

Cite This Article

Kişi, Ö., Akbıyık, R., Gürdal, M. (2024). Some results on $I_2$-deferred statistically convergent double sequences in fuzzy normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1474229

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (40)

  1. Agnew, R. P., On deferred Cesaro mean, Ann. Math., 33(3) (1932), 413–421. https://doi.org/10.2307/1968524
  2. Bag, T., Samanta, S. K., Fuzzy bounded linear operators, Fuzzy Sets Syst., 151(3) (2005), 513–547. https://doi.org/10.1016/j.fss.2004.05.004
  3. Cheng, S. C., Mordeson, J. N., Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), 429–436.
  4. Dağadur, I., Sezgek, Ş., Deferred Cesaro mean and deferred statistical convergence of double sequences, J. Inequal. Spec. Funct., 7(4) (2016), 118–136.
  5. Dağadur, I., Sezgek, Ş., Deferred statistical cluster points of double sequences, Math. Appl., 4(2) (2015), 77–90. https://doi.org/10.13164/ma.2015.06
  6. Das, N. R., Das, P., Fuzzy topology generated by fuzzy norm, Fuzzy Sets Syst., 107(3) (1999), 349–354. https://doi.org/10.1016/S0165-0114(97)00302-3
  7. Das, P., Kostyrko, P., Wilczynski, W., Malik, P., $I$ and $I^*$-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620. https://doi.org/10.2478/s12175-008-0096-x
  8. Et, M., Çınar, M., Şengül, H., Deferred statistical convergence in metric spaces, Conf. Proc. Sci. Tech., 2(3) (2019), 189-193.
  9. Et, M., Yılmazer, M. Ç., On deferred statistical convergence of sequences of sets, AIMS Math., 5(3) (2020), 2143–2152. https://doi.org/10.3934/math.2020142
  10. Fang, J. X., A note on the completions of fuzzy metric spaces and fuzzy normed spaces, Fuzzy Sets Syst., 131(3) (2002), 399–407. https://doi.org/10.1016/S0165-0114(02)00054-4
  11. Fast, H., Sur la convergence statistique, Colloq. Math., 2(3-4) (1951), 241–244.
  12. Felbin, C., Finite dimensional fuzzy normed linear space, Fuzzy Sets Syst., 48(2) (1992), 239–248. https://doi.org/10.1016/0165-0114(92)90338-5
  13. Fridy, J. A., Statistical limit points, Proc. Amer. Math. Soc., 118(4) (1993), 1187–1192. https://doi.org/10.2307/2160076
  14. Goetschel, R., Voxman, W., Elementary fuzzy calculus, Fuzzy Sets Syst., 18(1) (1986), 31–43. https://doi.org/10.1016/0165-0114(86)90026-6
  15. Gülle, E., Ulusu, U., Dündar, E., Tortop, Ş., $I_2$-deferred statistical convergence for sequences of sets, Filomat, 38(3) (2024), 891–901. https://doi.org/10.2298/FIL2403891G
  16. Hazarika, B., Alotaibi, A., Mohiuddine, S. A., Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24 (2020), 6613–6622. https://doi.org/10.1007/s00500-020-04805-y
  17. Katsaras, A. K., Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12(2) (1984), 143–154. https://doi.org/10.1016/0165-0114(84)90034-4
  18. Kişi, Ö., Gürdal, M., Savaş, E., On deferred statistical convergence of fuzzy variables, Appl. Appl. Math., 17(2) (2022), 1–20.
  19. Kişi, Ö., Huban, M. B., Gürdal, M., New results on $I_2$-statistically limit points and $I_2$-statistically cluster points of sequences of fuzzy numbers, J. Func. Spaces, 2021 (2021), Article ID 4602823, 6 pages. https://doi.org/10.1155/2021/4602823
  20. Kostyrko, P., Salat, T., Wilczyski, W., $I$-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  21. Kumar, V., Kumar, K., On the ideal convergence of sequences of fuzzy numbers, Inf. Sci., 178(24) (2008), 4670–4678. https://doi.org/10.1016/j.ins.2008.08.013
  22. Kumar, V., Sharma, A., Kumar, K., Singh, N., On $I$-limit points and I$$-cluster points of sequences of fuzzy numbers, Int. Math. Forum, 2 (2007), 2815–2822.
  23. Küçükaslan, M., Yilmaztürk, M., On deferred statistical convergence of sequences, Kyungpook Math. J., 56(2) (2016), 357–366. http://dx.doi.org/10.5666/KMJ.2016.56.2.357
  24. Matloka, M., Sequences of fuzzy numbers, Busefal, 28 (1986), 28–37.
  25. Mohiuddine, S. A., Asiri, A., Hazarika, B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48(5) (2019), 492–506. https://doi.org/10.1080/03081079.2019.1608985
  26. Mursaleen, M., Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1) (2003), 223–231. https://doi.org/10.1016/j.jmaa.2003.08.004
  27. Nanda, S., On sequences of fuzzy numbers, Fuzzy Sets Syst., 33(1) (1989), 123–126. https://doi.org/10.1016/0165-0114(89)90222-4
  28. Nuray, F., Savaş, E., Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 45(3) (1995), 269-273.
  29. Raj, K., Mohiuddine, S. A., Jasrotia, S., Characterization of summing operators in multiplier spaces of deferred Norlund summability, Positivity, 27 (2023), Article 9. https://doi.org/10.1007/s11117-022-00961-7
  30. Savaş, E., Das, P., A generalized statistical convergence via ideals, Appl. Math. Lett., 24(6) (2011), 826–830. https://doi.org/10.1016/j.aml.2010.12.022
  31. Savaş, E., Gürdal, M., $I$-statistical convergence in probabilistic normed spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 77(4) (2015), 195–204.
  32. Schoenberg, I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5) (1951), 361–375. https://doi.org/10.2307/2308747
  33. Şencimen, C., Pehlivan, S., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets Syst., 159(3) (2008), 361–370. https://doi.org/10.1016/j.fss.2007.06.008
  34. Şengül, H., Et, M., Işık, M., On $I$-deferred statistical convergence of order $\alpha$, Filomat, 33(9) (2019), 2833–2840. https://doi.org/10.2298/FIL1909833S
  35. Sezgek, Ş., Dağadur, I., On strongly deferred Cesaro mean of double sequences, J. Math. Anal., 8(3) (2017), 43–53.
  36. Tripathy, B. C., Debnath, S., Rakshit, D., On I$$-statistically limit points and $I$-statistically cluster poins of sequences of fuzzy numbers, Mathematica, 63(86)(1) (2021), 140–147. https://doi.org/10.24193/mathcluj.2021.1.13
  37. Ulusu, U., Gülle, E., Deferred Cesaro summability and statistical convergence for double sequences of sets, J. Intell. Fuzzy Syst., 42(4) (2022), 4095–4103. https://doi.org/10.3233/JIFS-212486
  38. Xiao, J., Zhu, X., On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets Syst., 125(2) (2002), 153-161. https://doi.org/10.1016/S0165-0114(00)00136-6
  39. Zadeh, L.A., Fuzzy sets, Infor. Control, 8(3) (1965), 338–353.
  40. Zygmund, A., Trigonometric Series, Cambridge University Press, New York, 1959.