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Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces

Yıl 2022, Cilt: 11 Sayı: 3, 233 - 246, 31.12.2022

Ahmet Özcan Aykut Or

https://doi.org/10.54187/jnrs.1198582

Öz

This paper proposes rough convergence and rough statistical convergence of a double sequence in intuitionistic fuzzy normed spaces. It then defines the rough statistical limit points and rough statistical cluster points of a double sequence in these spaces. Afterwards, this paper examines some of their basic properties. Finally, it discusses the need for further research.

Anahtar Kelimeler

Rough convergence Statistical convergence Rough statistical convergence Intuitionistic fuzzy normed spaces

Kaynakça

  • H. Fast, Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), (1951) 241-244.
  • H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicae, 2, (1951) 73-74.
  • A. Zygmund, Trigonometricheskii ryady, Moscow, Leningrad, Gostekhizdat, 1939.
  • M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, Journal of Mathematical Analysis and Applications, 288(1), (2003) 223-231.
  • H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis and Optimization, 22(1-2), (2001) 199-222.
  • S. Aytar, Rough statistical convergence, Numerical Functional Analysis and Optimization, 29(3-4), (2008) 291-303.
  • P. Malik, M. Maity, On rough convergence of double sequence in normed linear spaces, Bulletin of Theallahabad Mathematical Society, 28(1), (2013) 89-99.
  • P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Matematika, 27(1-2), (2016) 141-148.
  • U. Yamancı, M. Gürdal, I-statistically pre-cauchy double sequences, Global Journal of Mathematical Analysis, 2(4), (2014) 297-303.
  • Ö. Kişi, E. Dündar, Rough ${I}_{2}$-lacunary statistical convergence of double sequences, Journal of Inequalities and Applications, 2018, Article No: 230, (2018) 1-16.
  • S. Bulut, A. Or, ${I}$-statistical rough convergence of order $\alpha$, Journal of New Theory, (38), (2022) 34-41.
  • L. A. Zadeh, Fuzzy sets, Information Control, 8(3), (1965) 338-353.
  • S. C. Cheng, J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, in: P. P. Wang, J. Dai, J. C. Y. Tyan (Eds.), First International Conference on Fuzzy Theory and Technology Proceedings, Abstracts and Summaries 1992, University of North-Carolina/Duke University, USA, 1992, pp. 193-197.
  • T. Bag, S. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151(3), (2005) 513-547.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87-96.
  • K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33(1), (1989) 37-45.
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5), (2004) 1039-1046
  • R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals, 27(2), (2006) 331-344.
  • S. Karakuş, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals, 35(4), (2008) 763-769.
  • E. Savaş, M. Gürdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41, (2015) 289-294.
  • M. Mursaleen, S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals, 41(5), (2009) 2414-2421.
  • R. Antal, M. Chawla, V. Kumar, Rough statistical convergence in intuitionistic fuzzy normed spaces, Filomat, 35(13), (2021) 4405-4416.

Yıl 2022, Cilt: 11 Sayı: 3, 233 - 246, 31.12.2022

Ahmet Özcan Aykut Or

https://doi.org/10.54187/jnrs.1198582

Öz

Anahtar Kelimeler

Statistical convergence Rough statistical convergence Intuitionistic fuzzy normed spaces

Kaynakça

  • H. Fast, Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), (1951) 241-244.
  • H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicae, 2, (1951) 73-74.
  • A. Zygmund, Trigonometricheskii ryady, Moscow, Leningrad, Gostekhizdat, 1939.
  • M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, Journal of Mathematical Analysis and Applications, 288(1), (2003) 223-231.
  • H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis and Optimization, 22(1-2), (2001) 199-222.
  • S. Aytar, Rough statistical convergence, Numerical Functional Analysis and Optimization, 29(3-4), (2008) 291-303.
  • P. Malik, M. Maity, On rough convergence of double sequence in normed linear spaces, Bulletin of Theallahabad Mathematical Society, 28(1), (2013) 89-99.
  • P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Matematika, 27(1-2), (2016) 141-148.
  • U. Yamancı, M. Gürdal, I-statistically pre-cauchy double sequences, Global Journal of Mathematical Analysis, 2(4), (2014) 297-303.
  • Ö. Kişi, E. Dündar, Rough ${I}_{2}$-lacunary statistical convergence of double sequences, Journal of Inequalities and Applications, 2018, Article No: 230, (2018) 1-16.
  • S. Bulut, A. Or, ${I}$-statistical rough convergence of order $\alpha$, Journal of New Theory, (38), (2022) 34-41.
  • L. A. Zadeh, Fuzzy sets, Information Control, 8(3), (1965) 338-353.
  • S. C. Cheng, J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, in: P. P. Wang, J. Dai, J. C. Y. Tyan (Eds.), First International Conference on Fuzzy Theory and Technology Proceedings, Abstracts and Summaries 1992, University of North-Carolina/Duke University, USA, 1992, pp. 193-197.
  • T. Bag, S. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151(3), (2005) 513-547.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87-96.
  • K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33(1), (1989) 37-45.
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5), (2004) 1039-1046
  • R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals, 27(2), (2006) 331-344.
  • S. Karakuş, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals, 35(4), (2008) 763-769.
  • E. Savaş, M. Gürdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41, (2015) 289-294.
  • M. Mursaleen, S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals, 41(5), (2009) 2414-2421.
  • R. Antal, M. Chawla, V. Kumar, Rough statistical convergence in intuitionistic fuzzy normed spaces, Filomat, 35(13), (2021) 4405-4416.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ahmet Özcan 0000-0003-1458-9015

Aykut Or 0000-0001-5279-0057

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 11 Sayı: 3

Kaynak Göster

APA Özcan, A., & Or, A. (2022). Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Journal of New Results in Science, 11(3), 233-246. https://doi.org/10.54187/jnrs.1198582
AMA Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. Aralık 2022;11(3):233-246. doi:10.54187/jnrs.1198582
Chicago Özcan, Ahmet, ve Aykut Or. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science 11, sy. 3 (Aralık 2022): 233-46. https://doi.org/10.54187/jnrs.1198582.
EndNote Özcan A, Or A (01 Aralık 2022) Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Journal of New Results in Science 11 3 233–246.
IEEE A. Özcan ve A. Or, “Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces”, JNRS, c. 11, sy. 3, ss. 233–246, 2022, doi: 10.54187/jnrs.1198582.
ISNAD Özcan, Ahmet - Or, Aykut. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science 11/3 (Aralık 2022), 233-246. https://doi.org/10.54187/jnrs.1198582.
JAMA Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. 2022;11:233–246.
MLA Özcan, Ahmet ve Aykut Or. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science, c. 11, sy. 3, 2022, ss. 233-46, doi:10.54187/jnrs.1198582.
Vancouver Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. 2022;11(3):233-46.
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