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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces

Ekrem Savaş0000-0003-2135-3094
Ulas Yamanci0000-0002-4709-0993
Mehmet Gürdal0000-0003-0866-1869
Pages
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Publication Date
2019-08-01
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AI Summary & Key Takeaways

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

Also, we study the relationship between them and obtain some interesting results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce new concepts of I-statistical convergence and I-lacunary statistical convergence using weighted density via modulus functions.
📊
Key Findings & Data:In this paper, we introduce new concepts of I-statistical convergence and I-lacunary statistical convergence using weighted density via modulus functions.
💡
Conclusion & Impact:Also, we study the relationship between them and obtain some interesting results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:I-statistical convergence · I-lacunary statistical convergence · 2-normed spaces

Abstract

In this paper, we introduce new concepts of I-statistical convergence and I-lacunary statistical convergence using weighted density via modulus functions. Also, we study the relationship between them and obtain some interesting results.

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Cite This Article

Savaş, E., Yamanci, U., Gürdal, M. (2019). I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.573396

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References (26)

  1. Balcerzak, M., Das, P., Filipczak, M. and Swaczyna, J., Generalized kinds of density and the associated ideals, Acta Math. Hungar. 147, (2015), 97--115.
  2. Bose, K., Das, P. and Kwela, A., Generating new ideals using weighted density via modulus functions, Indag. Math. 29(5), (2018), 1196--1209.
  3. Das, P., Savaş E. and Ghosal, S., On generalized of certain summability methods using ideals, Appl. Math. Lett. 26, (2011), 1509--1514.
  4. Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241--244.
  5. Fridy, J. A. and Orhan, C., Lacunary statistical convergence, Pacific J. Math. 160, (1993), 43--51.
  6. Gähler, S., 2-metrische Räume und ihre topologische struktur, Math. Nachr. 26, (1993), 115--148.
  7. Gürdal, M., On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1), (2006), 85--91.
  8. Gürdal, M. and Açık, I., On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 2(1), (2008), 349--354.
  9. Gürdal, M. and Yamancı, U., Statistical convergence and some questions of operator theory, Dynam. Syst. Appl. 24, (2015), 305--312.
  10. Kostyrko, P.,Šalát, T. and Wilezynski, W., I-Convergence, Real Anal. Exchange 26(2), (2000), 669--686.
  11. Mursaleen, M. and Alotaibi, A., On I-convergence in random 2-normed space, Math. Slovaca 61(6), (2011), 933--940.
  12. Nabiev, A., Pehlivan, S. and Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math. 11(2), (2007), 569--576.
  13. Şahiner, A., Gürdal, M., Saltan, S. and Gunawan, H., Ideal Convergence in 2-normed Spaces, Taiwanese J. Math. 11(4), (2007), 1477--1484.
  14. Savaş, E., On lacunary strong σ-convergence, Indian J. Pure Appl. Math. 21, (1990), 359--365.
  15. Savaş, E. and Karakaya, V., Some new sequence spaces defined by lacunary sequences, Math. Slovaca 57, (2007), 393--399.
  16. Savaş, E. and Patterson, R. F., Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl. 11, (2009), 610--615.
  17. Savaş, E. and Das, P., A generalized statistical convergence via ideals, Appl. Math. Letters 24, (2011), 826--830.
  18. Savaş, E., Das, P. and Dutta, S., A note on strong matrix summability via ideals, Appl. Math Letters 25, (2012) 733--738.
  19. Savaş, E., On I-lacunary statistical convergence of order α for sequences of sets, Filomat 29, (2015), 1223--1229.
  20. Schoenberg, I. J., The integrability of certain functions and related summability methods, Am. Math. Mon. 66, (1959), 361--375.
  21. Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, (1951), 73--74.
  22. Ulusu, U. and Nuray, F., Lacunary statistical convergence of sequence of sets, Progress Appl. Math. 4, (2012), 99--109.
  23. Ulusu, U. and Dündar, E., I-lacunary statistical convergence of sequences of sets, Filomat 28(8), (2014), 1567--1574.
  24. Yamancı, U. and Gürdal, M., I-statistical convergence in 2-normed space, Arab J. Math. Sci. 20(1), (2014), 41--47.
  25. Yamancı, U. and Gürdal, M., Statistical convergence and operators on Fock space, New York J. Math. 22, (2016), 199--207.
  26. Yegül, S. and Dündar, E., On statistical convergence of sequences of functions in 2-normed spaces, J. Classical Anal. 10(1), (2017), 49--57.