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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2018 / Cilt: 18 - Sayı: 3

On Lacunary I 2 -Convergence Of Double Sequences And Some Properties In Fuzzy n-Normed Space

Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary I 2 -Yakınsaklığı ve Bazı Özellikleri Üzerine

Muhammed Recai TÜRKMEN
Pages
868–877
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

Finally, in fuzzy n-normed spaces, the concept of Fnθ 2 -Cauchy and FnI 2θ -Cauchy and the theorems related to these concepts are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, firstly lacunary ideal convergence of double sequences is introduced in fuzzy n-normed spaces.
📊
Key Findings & Data:And then basic definitions and theorems about lacunary ideal convergence for double sequences are given in fuzzy n-normed spaces.
💡
Conclusion & Impact:Finally, in fuzzy n-normed spaces, the concept of Fnθ 2 -Cauchy and FnI 2θ -Cauchy and the theorems related to these concepts are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, firstly lacunary ideal convergence of double sequences is introduced in fuzzy n-normed spaces. And then basic definitions and theorems about lacunary ideal convergence for double sequences are given in fuzzy n-normed spaces. Secondly, we introduce the concept of θ-convergence of double sequences in fuzzy n-normed spaces, and the relation between θ-convergence and lacunary ideal convergence is investigated for double sequences in fuzzy n-normed spaces. Finally, in fuzzy n-normed spaces, the concept of Fnθ 2 -Cauchy and FnI 2θ -Cauchy and the theorems related to these concepts are given.

Özet

Bu çalışmada çift dizilerin lacunary ideal yakınsaklığı fuzzy n-norm kullanarak yeniden tanımlanmıştır.Çalışmada ilk olarak fuzzy n-normlu uzaylarda çift diziler için lacunary ideal yakınsaklık kavramına yerverilmiş, daha sonra bu yakınsama ile ilgili temel teoremlere değinilmiştir. İkinci olarak θ-yakınsaklıkkavramını fuzzy n-normlu uzaylarda çift diziler için tanıtıp, θ-yakınsaklık ile lacunary ideal yakınsaklıkarasındaki ilişki fuzzy n-normlu uzaylarda çift diziler için incelenmiştir. Son olarak, fuzzy n-normluuzaylarda Fnθ 2 -Cauchy ve FnI 2θ -Cauchy kavramları ve bu kavramlarla ilgili teoremlerin ifadeleriverilmiştir.

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Cite This Article

TÜRKMEN, M. R. (2022). On Lacunary I 2 -Convergence Of Double Sequences And Some Properties In Fuzzy n-Normed Space. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 18 - Sayı: 3, 868–877. https://ajindex.com/articles/429949

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References (16)

  1. Bag, T. and Samanta, S. K., 2008. Fixed point theorems in Felbin’s type fuzzy normed linear spaces. J. Fuzzy Math., 16(1), 243–260.
  2. Debnath, P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers &Mathematics With Applications, 63(3), 708–715.
  3. Diamond, P. and Kloeden, P., 1994. Metric Spaces of Fuzzy Sets-Theory and Applications. World Scientific Publishing, Singapore. Dündar, E. and Talo, Ö., 2013a. I 2 -convergence of double sequences of fuzzy numbers. Iranian Journal of Fuzzy Systems, 10(3), 37–50.
  4. Dündar, E. and Talo, Ö., 2013b. I 2 -Cauchy Double Sequences of Fuzzy Numbers. Gen. Math. Notes, 16(2), 103-114.
  5. Dündar, E. and Altay, B., 2014. I 2 -convergence and I 2 -Cauchy of double sequences. Acta Mathematica Scientia, 34(2), 343–353.
  6. Dündar, E., Ulusu, U. and Pancaroğlu, N., 2016. Strongly I 2 -Lacunary Convergence and I 2 - Lacunary Cauchy Double Sequences of Sets. The Aligarh Bulletin of Mathematics, 35(1,2), 1–15.
  7. Fast, H., 1951. Sur la convergence statistique Colloq. Math., 2, 241–244.
  8. Felbin, C., 1992. Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239–248.
  9. Fridy, J. A., 1985. On statistical convergence. Analysis, 5, 301–313.
  10. Fridy, J. A. and Orhan, C., 1993a. Lacunary statistical summability. Jour Math. Anal. Appl., 173(2), 497-504.
  11. Fridy, J. A. and Orhan, C., 1993b. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43--51. Hazarika, B., 2013. On ideal convergent sequences in fuzzy normed linear spaces. Afrika Matematika, 25(4), 987–999.
  12. Hazarika, B. and Kumar, V., 2014. Fuzzy real valued I-convergent double sequences in fuzzy normed spaces. Journal of Intelligent and Fuzzy Systems, 26, 2323–2332.
  13. Hazarika, B., 2016. Lacunary ideal convergence of multiple sequences. Journal of the Egyptian Mathematical Society, 24, 54–59.
  14. Kara, E. E. and İlkhan, M., 2016. Lacunary I- convergent and lacunary I -bounded sequence spaces defined by an Orlicz function. Electron. J. Math. Anal. Appl., 4(2), 150-159.
  15. Kara, E. E., Dastan, M. and İlkhan, M., 2017. On Lacunary ideal convergence of some sequences. New Trends in Mathematical Sciences, 5(1), 234-242.
  16. Katsaras, A. K., 1984. Fuzzy topological vector spaces. Fuzzy sets and systems, 12, 143—154. Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. I- Convergence. Real Analysis Exchange, 26(2), 669—686. Kostyrko, P., Macaj, M., Šalát, T. and Sleziak, M., 2005. I-Convergence and Extermal I-limits points. Mathematica Slovaca, 5