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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 1

Lacunary invariant statistical equivalence for double set sequences

Uğur Ulusu(SİVAS CUMHURİYET UNIVERSITY)0000-0001-7658-6114
Erdinç Dündar(AFYON KOCATEPE UNIVERSITY)0000-0002-0545-7486
Nimet Pancaroğlu Akın(AFYON KOCATEPE UNIVERSITY)0000-0003-2886-3679
Pages
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Publication Date
2022-03-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, we investigate some relations between these new asymptotical equivalence notions.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce the notions of asymptotical strong σ 2 σ2 -equivalence, asymptotical σ 2 σ2 -statistical equivalence, asymptotical lacunary strong σ 2 σ2 -equivalence and asymptotical lacunary σ 2 σ2 -statistical equivalence in the Wijsman sense for double set sequences.
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Key Findings & Data:In this paper, we introduce the notions of asymptotical strong σ 2 σ2 -equivalence, asymptotical σ 2 σ2 -statistical equivalence, asymptotical lacunary strong σ 2 σ2 -equivalence and asymptotical lacunary σ 2 σ2 -statistical equivalence in the Wijsman sense for double set sequences.
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Conclusion & Impact:Also, we investigate some relations between these new asymptotical equivalence notions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotical equivalence · double lacunary sequence · invariant mean

Abstract

In this paper, we introduce the notions of asymptotical strong σ 2 σ2 -equivalence, asymptotical σ 2 σ2 -statistical equivalence, asymptotical lacunary strong σ 2 σ2 -equivalence and asymptotical lacunary σ 2 σ2 -statistical equivalence in the Wijsman sense for double set sequences. Also, we investigate some relations between these new asymptotical equivalence notions.

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Cite This Article

Ulusu, U., Dündar, E., Akın, N. P. (2022). Lacunary invariant statistical equivalence for double set sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 1. https://doi.org/10.31801/cfsuasmas.903988

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References (19)

  1. Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(3) (1900), 289–321. https://doi.org/10.1007/BF01448977
  2. Moricz, F., Statistical convergence of multiple sequences, Arc. Math, 81(1) (2003), 82–89. https://doi.org/10.1007/s00013-003-0506-9
  3. 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
  4. Patterson, R. F., Savaş, E., Lacunary statistical convergence of double sequences, Math. Commun. 10(1) (2005), 55–61.
  5. Savaş, E., Patterson, R. F., Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl., 11(4) (2009), 610–615.
  6. Patterson, R. F., Rates of convergence for double sequences, Southeast Asian Bull. Math., 26(3) (2003), 469–478. https://doi.org/10.1007/s10012-002-0469-y
  7. Wijsman, R. A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1) (1964), 186–188. https://doi.org/10.1090/S0002-9904-1964-11072-7
  8. Baronti, M., Papini, P., Convergence of Sequences of Sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986.
  9. Nuray, F., Rhoades, B. E., Statistical convergence of sequences of sets, Fasc. Math., 49(2) (2012), 87–99. https://doi.org/10.3968/j.pam.1925252820120402.2264
  10. Beer, G., Wijsman convergence: A survey, Set-Valued Anal., 2(1) (1994), 77–94. https://doi.org/10.1007/BF01027094
  11. Nuray, F., Ulusu, U., Dündar, E., Lacunary statistical convergence of double sequences of sets, Soft Comput., 20(7) (2016), 2883–2888. https://doi.org/10.1007/s00500-015-1691-8
  12. Nuray, F., Ulusu, U., Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform., 28(2) (2019), 143–150. https://doi.org/10.37193/CMI.2019.02.06
  13. Nuray, F., Dündar, E., Ulusu, U., Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., 16(1) (2021), 55–64. https://doi.org/10.29252/ijmsi.16.1.55
  14. Nuray, F., Patterson, R. F., Dündar, E., Asymptotically lacunary statistical equivalence of double sequences of sets, Demonstratio Math., 49(2) (2016), 183–196. https://doi.org/10.1515/dema-2016-0016
  15. Ulusu, U., Dündar, E., Asymptotically I2-lacunary statistical equivalence of double sequences of sets, J. Ineq. Spec. Funct., 7(2) (2016), 44–56.
  16. Ulusu, U., Gülle, E., Wijsman asymptotical I2-statistically equivalent double set sequences of order η, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 854–862. https://doi.org/10.31801/cfsuasmas.695309
  17. Gülle, E., Ulusu, U., Wijsman asymptotical I2-lacunary statistically equivalence of order η for double set sequences, J. Appl. Math. Inform., (in press) (2021).
  18. Pancaroğlu, N., Nuray, F., Savaş, E., On asymptotically lacunary invariant statistical equivalent set sequences, AIP Conf. Proc., 1558(1) (2013), 780–781. https://doi.org/10.1063/1.4825609
  19. Ulusu, U., Nuray, F., On asymptotically lacunary statistical equivalent set sequences, J. Math., 2013(Article ID 310438) (2013), 5 pages. https://doi.org/10.1155/2013/310438