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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2019 / Cilt: 19 - Sayı: 1

f-Asymptotically 𝓘𝟐 𝝈 -Equivalence of Double Sequences of Sets

Çift Küme Dizilerinin f-Asimptotik 𝓘𝟐 𝝈 -Denkliği

Erdinç DÜNDAR
Nimet P. AKIN
Pages
79–86
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

Also we investigate relationships between asymptotically ℐ2 𝜎 -statistical equivalence and strongly 𝑓-asymptotically ℐ2 𝜎 -equivalence.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, first, we present the concepts of strongly asymptotically ℐ2 𝜎 -equivalence, 𝑓-asymptotically ℐ2 𝜎 -equivalence, strongly 𝑓-asymptotically ℐ2 𝜎 -equivalence for double sequences of sets.
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Key Findings & Data:After, we present asymptotically ℐ2 𝜎 -statistical equivalence for double sequences of sets.
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Conclusion & Impact:Also we investigate relationships between asymptotically ℐ2 𝜎 -statistical equivalence and strongly 𝑓-asymptotically ℐ2 𝜎 -equivalence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, first, we present the concepts of strongly asymptotically ℐ2 𝜎 -equivalence, 𝑓-asymptotically ℐ2 𝜎 -equivalence, strongly 𝑓-asymptotically ℐ2 𝜎 -equivalence for double sequences of sets. Then, we investigated some properties and relationships among this new concepts. After, we present asymptotically ℐ2 𝜎 -statistical equivalence for double sequences of sets. Also we investigate relationships between asymptotically ℐ2 𝜎 -statistical equivalence and strongly 𝑓-asymptotically ℐ2 𝜎 -equivalence.

Özet

Bu çalışmada, ilk olarak, çift küme dizilerinin kuvvetli asimptotik ℐ2 𝜎 -denkliği, 𝑓-asimptotik ℐ2 𝜎 -denkliği, kuvvetli 𝑓-asimptotik ℐ2 𝜎 -denkliği kavramları tanımlandı. Daha sonra bu kavramlar arasındaki ilişkiler ve bazı özellikler incelendi. İkinci olarak, yine çift küme dizileri için asimptotik ℐ2 𝜎 -istatistiksel denklik kavramı tanımlandı. Ayrıca, asimptotik ℐ2 𝜎 -istatistiksel denklik kavramı ve kuvvetli 𝑓-asimptotik ℐ2 𝜎 - denkliği kavramı arasındaki ilişkiler incelendi.

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Cite This Article

DÜNDAR, E., AKIN, N. P. (2022). f-Asymptotically 𝓘𝟐 𝝈 -Equivalence of Double Sequences of Sets. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 19 - Sayı: 1, 79–86. https://ajindex.com/articles/429895

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References (11)

  1. Baronti M., and Papini P., 1986. Convergence of sequences of sets. In: Methods of functional analysis in approximation theory (pp. 133-155), ISNM 76, Birkhäuser, Basel. Beer G., 1985. On convergence of closed sets in a metric space and distance functions. Bulletin of the Australian Mathematical Society, 31, 421- 432. Beer G., 1994. Wijsman convergence: A survey. SetValued Analysis, 2, 77-94.
  2. Das, P., Kostyrko, P., Wilczyński, W. and Malik, P., 2008. ℐ and ℐ ∗-convergence of double sequences. Mathematica Slovaca, 58(5), 605-620.
  3. Dündar, E., Ulusu, U. and Pancaroğlu, N., 2016. Strongly ℐ2-convergence and ℐ2-lacunary Cauchy double sequences of sets. The Aligarh Bulletin of Mathematics, 35(1-2), 1-15.
  4. Dündar, E., Ulusu, U. and Aydın, B., 2017. ℐ2- lacunary statistical convergence of double sequences of sets. Konuralp Journal of Mathematics, 5(1), 1-10.
  5. Dündar, E., Ulusu, U. and Nuray, F., On asymptotically ideal invariant equivalence of double sequences, (In review). Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
  6. Khan, V. A. and Khan, N., 2013. On Some ℐ-Convergent Double Sequence Spaces Defined by a Modulus Function. Engineering, 5, 35-40.
  7. Kılınç, G. and Solak, İ., 2014. Some Double Sequence Spaces Defined by a Modulus Function. General Mathematics Notes, 25(2), 19-30.
  8. Kişi Ö., Gümüş H. and Nuray F., 2015. ℐAsymptotically lacunary equivalent set sequences defined by modulus function. Acta Universitatis Apulensis, 41, 141-151.
  9. Kişi, Ö. and Nuray, F., 2013. A new convergence for sequences of sets. Abstract and Applied Analysis, 2013, 6 pages. Kostyrko P., Šalát T. and Wilczyński W., 2000. ℐ-Convergence. Real Analysis Exchange, 26(2), 669-686. Kumar V. and Sharma A., 2012. Asymptotically lacunary equivalent sequences defined by ideals and modulus function. Mathematical Sciences, 6(23), 5 pages. Lorentz G., 1948. A contribution to the theory of divergent sequences. Acta Mathematica, 80, 167-190. Maddox J., 1986. Sequence spaces defined by a modulus. Mathematical Proceedings of the Cambridge Philosophical Society, 100, 161-166.
  10. Marouf, M., 1993. Asymptotic equivalence and summability. Int. J. Math. Math. Sci., 16(4), 755- 762. Mursaleen, M., 1983. Matrix transformation between some new sequence spaces. Houston Journal of Mathematics, 9, 505-509.
  11. Mursaleen, M. and Edely, O. H. H., 2009. On the invariant mean and statistical convergence. Applied Mathematics Letters, 22(11), 1700- 1704. Nakano H., 1953. Concave modulars. Journal