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Journals / Konuralp Journal of Mathematics / 2020 / Cilt: 8 - Sayı: 2

Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets

Esra GÜLLE
Uğur ULUSU
Pages
322–328
Publication Date
2020-10-27
DOI
—
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AI Summary & Key Takeaways

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

Furthermore, we examine the existence of the relations between some of these new convergence types, too.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we give definitions of Wijsman quasi-lacunary invariant convergence, Wijsman quasi-strongly lacunary invariant convergence and Wijsman quasi-strongly $q$-lacunary invariant convergence for sequences of sets.
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Key Findings & Data:Also we define Wijsman quasi-lacunary invariant statistical convergence.
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Conclusion & Impact:Furthermore, we examine the existence of the relations between some of these new convergence types, too.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quasi-invariant convergence · lacunary sequence · statistical convergence

Abstract

In this study, we give definitions of Wijsman quasi-lacunary invariant convergence, Wijsman quasi-strongly lacunary invariant convergence and Wijsman quasi-strongly $q$-lacunary invariant convergence for sequences of sets. Also we define Wijsman quasi-lacunary invariant statistical convergence. Then, we examine the existence of the relations among these new convergence types and some convergence types for sequences of sets given before. Furthermore, we examine the existence of the relations between some of these new convergence types, too.

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Cite This Article

GÜLLE, E., ULUSU, U. (2020). Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp Journal of Mathematics, Cilt: 8 - Sayı: 2, 322–328. https://ajindex.com/articles/786433

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References (21)

  1. Baronti, M. and Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986
  2. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421–432
  3. G. Beer, Wijsman convergence: A survey, Set-Valued Analysis 2(1-2) (1994), 77–94
  4. J.S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8(1-2) (1988), 47–64
  5. M. Et and H. Sengul, On (Dm; I)-lacunary statistical convergence of order a, J. Math. Anal. 7(5) (2016), 78–84
  6. H. Fast, Sur la convergence statistique, Colloq. Math. 2(3-4) (1951), 241–244
  7. J.A. Fridy, On statistical convergence, Analysis 5(4) (1985), 301–314
  8. J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Mathematics 160(1) (1993), 43–51
  9. E. G¨ulle and U. Ulusu, Wijsman quasi-invariant convergence, Creat. Math. Inform. 28(2) (2019), 113–120
  10. D. Hajdukovic, Quasi-almost convergence in a normed space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 36–41
  11. M. Mursaleen, Invariant mean and some matrix transformations, Thamkang J. Math. 10 (1979), 183–188
  12. M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2) (1983), 77–86
  13. M. Mursaleen and O.H.H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22(11) (2009), 1700–1704
  14. F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99
  15. F. Nuray, Quasi-invariant convergence in a normed space, Annals of the University of Craiova-Mathematics and Computer Science Series 41(1) (2014), 1–5
  16. N. Pancaroglu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress in Applied Mathematics 5(2) (2013), 23–29
  17. N. Pancaroglu and F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications 3(2) (2013), 71–78
  18. N. Pancaroglu Akın, E. D¨undar and U. Ulusu, Wijsman lacunary I-invariant convergence of sequences of sets, Proc. Nat. Acad. Sci. India Sect. A (accepted)
  19. R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1) (1963), 81–94
  20. E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8
  21. E. Savas, On lacunary strong s-convergence, Indian J. Pur