Honam Mathematical Journal (호남수학학술지)

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DEFERRED INVARIANT STATISTICAL CONVERGENCE OF ORDER 𝜂 FOR SET SEQUENCES

  • Gulle, Esra (Department of Mathematics, Afyon Kocatepe University)
  • Received : 2021.10.07
  • Accepted : 2021.10.25
  • Published : 2022.03.25
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Abstract

In this paper, we introduce the concepts of Wijsman invariant statistical, Wijsman deferred invariant statistical and Wijsman strongly deferred invariant convergence of order 𝜂 (0 < 𝜂 ≤ 1) for set sequences. Also, we investigate some properties of these concepts and some relationships between them.

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References

  1. R.P. Agnew, On deferred Cesaro mean, Comm. Ann. Math. 33 (1932), 413-421. https://doi.org/10.2307/1968524
  2. M. Altinok, B. Inan, and M. Kucukaslan, On deferred statistical convergence of sequences of sets in metric space, Turk. J. Math. Comput. Sci. 3 (2015), no. 1, 1-9.
  3. G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2 (1994), 77-94. https://doi.org/10.1007/BF01027094
  4. R. Colak, Statistical convergence of order α, In: Modern Methods in Analysis and Its Applications (pp. 121-129), Anamaya Publishers, New Delhi, 2010.
  5. E. Dundar, N. Pancaroglu Akin, and U. Ulusu, Wijsman lacunary $\mathcal{I}$-invariant convergence of sequences of sets, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (2020), 1-6, https://doi.org/10.1007/s40010-020-00694-w.
  6. M. Et and M.C,. Yilmazer, On deferred statistical convergence of sequences of sets, AIMS Mathematics 5 (2020), no. 3, 2143-2152. https://doi.org/10.3934/math.2020142
  7. M. Et, M. Cinar, and H. Sengul Kandemir, Deferred statistical convergence of order α in metric spaces, AIMS Mathematics 5 (2020), no. 4, 3731-3740. https://doi.org/10.3934/math.2020241
  8. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  9. A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2001), no. 1, 129-138. https://doi.org/10.1216/rmjm/1030539612
  10. E. Gulle and U. Ulusu, Wijsman quasi-invariant convergence, Creat. Math. Inform. 28 (2019), no. 2, 113-120. https://doi.org/10.37193/CMI.2019.02.03
  11. E. Gulle and U. Ulusu, Quasi-lacunary invariant statistical convergence of sequences of sets, Konuralp Journal of Mathematics 8 (2020), no. 2, 322-328.
  12. M. Gurdal and U. Yamanci, Statistical convergence and some questions of operator theory, Dynamic Systems and Applications 24 (2015), 305-312.
  13. M. Ku,cukaslan and M. Yilmazturk, On deferred statistical convergence of sequences, Kyungpook Math. J. 56 (2016), 357-366. https://doi.org/10.5666/KMJ.2016.56.2.357
  14. M. Mursaleen and O.H.H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009), no. 11, 1700-1704. https://doi.org/10.1016/j.aml.2009.06.005
  15. F. Nuray, Strongly deferred invariant convergence and deferred invariant statistical convergence, Journal of Computer Science and Computational Mathematics 10 (2020), no. 1, 1-6. https://doi.org/10.20967/jcscm.2020.01.001
  16. F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87-99.
  17. F. Nuray, U. Ulusu, and E. Dundar, Lacunary statistical convergence of double sequences of sets, Soft Comput. 20 (2016), no. 7, 2883-2888. https://doi.org/10.1007/s00500-015-1691-8
  18. F. Nuray and U. Ulusu, Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform. 28 (2019), no. 2, 143-150. https://doi.org/10.37193/CMI.2019.02.06
  19. P. Pancaroglu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress in Applied Mathematics 5 (2013), no. 2, 23-29.
  20. R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81-94. https://doi.org/10.1215/S0012-7094-63-03009-6
  21. E. Sava,s and F. Nuray, On σ-statistically convergence and lacunary σ-statistically convergence, Mathematica Slovaca 43 (1993), no. 3, 309-315.
  22. E. Sava,s, U. Yamanci, and M. Gurdal, $\mathcal{I}$-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2019), no. 2, 2324-2332.
  23. P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104-110. https://doi.org/10.1090/S0002-9939-1972-0306763-0
  24. U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics 4 (2012), no. 2, 99-109.
  25. U. Ulusu and F. Nuray, Lacunary $\mathcal{I}$-invariant convergence, Cumhuriyet Science Journal 41 (2020), no. 3, 617-624. https://doi.org/10.17776/csj.689877
  26. U. Ulusu and E. Dundar, $\mathcal{I}$-lacunary statistical convergence of sequences of sets, Filomat 28 (2014), 1567-1574. https://doi.org/10.2298/FIL1408567U
  27. U. Ulusu and E. Gulle, Some statistical convergence types of order α for double set sequences, Facta Univ. Ser. Math. Inform. 35 (2020), no. 3, 595-603.
  28. U. Yamanci and M. Gurdal, Statistical convergence and operators on Fock space, New York Journal of Mathematics 22 (2016), 199-207.
  29. U. Yamanci, A.A. Nabiev and M. Gurdal, Statistically localized sequences in 2-normed spaces, Honam Mathematical J. 42 (2020), no. 1, 161-173. https://doi.org/10.5831/HMJ.2020.42.1.161