SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

Wijsman asymptotical I_2-statistically equivalent double set sequences of order η

Uğur Ulusu(SİVAS CUMHURİYET UNIVERSITY)0000-0001-7658-6114
Esra Gülle(AFYON KOCATEPE UNIVERSITY)0000-0001-5575-2937
Pages
—
Publication Date
2020-06-30
🏛️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)

Also, we investigate some properties of these notions and some relationships between them.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present notions of Wijsman asymptotical I₂-statistically equivalence of order η, Wijsman asymptotical I₂-Cesàro equivalence of order η and Wijsman asymptotical strongly p-I₂-Cesàro equivalence of order η for double set sequences where 0<η≤1.
📊
Key Findings & Data:In this study, we present notions of Wijsman asymptotical I₂-statistically equivalence of order η, Wijsman asymptotical I₂-Cesàro equivalence of order η and Wijsman asymptotical strongly p-I₂-Cesàro equivalence of order η for double set sequences where 0<η≤1.
💡
Conclusion & Impact:Also, we investigate some properties of these notions and some relationships between them.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Wijsman convergence · Asymptotical equivalence · Cesàro summability

Abstract

In this study, we present notions of Wijsman asymptotical I₂-statistically equivalence of order η, Wijsman asymptotical I₂-Cesàro equivalence of order η and Wijsman asymptotical strongly p-I₂-Cesàro equivalence of order η for double set sequences where 0<η≤1. Also, we investigate some properties of these notions and some relationships between them.

🔖

Cite This Article

Ulusu, U., Gülle, E. (2020). Wijsman asymptotical I_2-statistically equivalent double set sequences of order η. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.695309

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (35)

  1. Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289--321.
  2. Mursaleen, M., Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223--231.
  3. Das, P., Kostyrko, P., Wilczyński, W., Malik, P., I and I^{∗}-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605--620.
  4. Bhunia, S., Das, P., Pal, S.K., Restricting statistical convergence, Acta Mathematica Hungarica, 134(1-2) (2012), 153--161
  5. Çolak, R., Altın, Y., Statistical convergence of double sequences of order α, Journal of Function Spaces and Applications, 2013(Article ID 682823) (2013), 5 pages.
  6. Savaş, E., Double almost statistical convergence of order α, Advances in Difference Equations, 2013(62) (2013), 9 pages.
  7. Altın, Y., Çolak, R., Torgut, B., I₂(u)-convergence of double sequences of order (α,β), Georgian Mathematical Journal, 22(2) (2015), 153--158.
  8. Patterson, R.F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2002), 469--478.
  9. Kavita, K., Sharma, A., Kumar, V., On generelized asymptotically equivalent double sequences through (V,λ,μ)-summability, Acta Universitatis Matthiae Belii, series Mathematics, 2013 (2013), 9 pages.
  10. Hazarika, B., Kumar, V., On asymptotically double lacunary statistical equivalent sequences in ideal context, Journal of Inequalities and Applications, 2013(543) (2013), 15 pages.
  11. Esi, A., Açıkgöz, M., On λ₂-asymptotically double statistical equivalent sequences, Int. J. Nonlinear Anal. Appl., 5(2) (2014), 16--21.
  12. Baronti, M., Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133--155), Birkhäuser, Basel, 1986.
  13. Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2 (1994), 77--94.
  14. Wijsman, R.A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70 (1964), 186--188.
  15. Nuray, F., Ulusu, U., Dündar, E., Cesàro summability of double sequences of sets, Gen. Math. Notes, 25(1) (2014), 8--18.
  16. Nuray, F., Dündar, E., Ulusu, U., Wijsman I₂-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2 (2014) 35--39.
  17. Dündar, E., Ulusu, U., Aydın, B., I₂-lacunary statistical convergence of double sequences of sets, Konuralp Journal of Mathematics, 5(1) (2017), 1--10.
  18. Ulusu, U., Dündar, E., Gülle, E., I₂-Cesàro summability of double sequences of sets, Palestine Journal of Mathematics, 9(1) (2020), 561--568.
  19. Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., (in press).
  20. Ulusu, U., Gülle, E., Some statistical convergence types for double set sequences of order α, Facta Univ. Ser. Math. Inform., (in press).
  21. Nuray, F., Patterson, R.F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Mathematica, 49(2) (2016), 183--196.
  22. Ulusu, U., Dündar, E., Asymptotically I₂-lacunary statistical equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(2) (2016), 44--56.
  23. Ulusu, U., Dündar, E., Aydın, B., Asymptotically I₂-Cesàro equivalence of double sequences of sets, Journal of Inequalities and Special Functions, 7(4) (2016), 225--234.
  24. Gülle, E., Double Wijsman asymptotically statistical equivalence of order α, Journal of Intelligent and Fuzzy Systems, 38(2) (2020), 2081--2087.
  25. Kostyrko, P., Šalát, T., Wilczyński, W., I-convergence, Real Anal. Exchange, 26(2) (2000), 669--686.
  26. Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 2013(Article ID 310438) (2013), 5 pages.
  27. Kişi, Ö., Nuray, F., On S_{λ}(I)-asymptotically statistical equivalence of sequence of sets, ISRN Mathematical Analysis, 2013(Article ID 602963) (2013), 6 pages.
  28. Das, P., Savaş, E., On I-statistical and I-lacunary statistical convergence of order α, Bull. Iranian Math. Soc., 40(2) (2014), 459--472.
  29. Et, M. and Şengül, H., Some Cesàro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8) (2014), 1593--1602.
  30. Sever, Y., Ulusu, U., Dündar, E., On strongly I and I^{∗}-lacunary convergence of sequences of sets, AIP Conference Proceedings, 2014(1611) (2014), 357--362.
  31. Ulusu, U., Dündar, E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567--1574.
  32. Savaş, E., On I-lacunary statistical convergence of order α for sequences of sets, Filomat, 29(6) (2015), 1223--1229.
  33. Savaş, E., Asymptotically I-lacunary statistical equivalent of order α for sequences of sets, Journal of Nonlinear Sciences and Applications, 10 (2017), 2860--2867.
  34. Şengül, H. and Et, M., On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8) (2017), 2403--2412.
  35. Şengül, H., On Wijsman I-lacunary statistical equivalence of order (η,μ), Journal of Inequalities and Special Functions, 9(2) (2018), 92--101.