Research Article
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Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces

Year 2022, Volume: 11 Issue: 3, 233 - 246, 31.12.2022
https://doi.org/10.54187/jnrs.1198582
https://izlik.org/JA43ZA53ZN

Abstract

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.

References

  • 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.

Year 2022, Volume: 11 Issue: 3, 233 - 246, 31.12.2022
https://doi.org/10.54187/jnrs.1198582
https://izlik.org/JA43ZA53ZN

Abstract

References

  • 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.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ahmet Özcan 0000-0003-1458-9015

Aykut Or 0000-0001-5279-0057

Publication Date December 31, 2022
DOI https://doi.org/10.54187/jnrs.1198582
IZ https://izlik.org/JA43ZA53ZN
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

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 1.Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. 2022;11(3):233-246. doi:10.54187/jnrs.1198582
Chicago Özcan, Ahmet, and Aykut Or. 2022. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science 11 (3): 233-46. https://doi.org/10.54187/jnrs.1198582.
EndNote Özcan A, Or A (December 1, 2022) Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Journal of New Results in Science 11 3 233–246.
IEEE [1]A. Özcan and A. Or, “Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces”, JNRS, vol. 11, no. 3, pp. 233–246, Dec. 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 (December 1, 2022): 233-246. https://doi.org/10.54187/jnrs.1198582.
JAMA 1.Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. 2022;11:233–246.
MLA Özcan, Ahmet, and Aykut Or. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science, vol. 11, no. 3, Dec. 2022, pp. 233-46, doi:10.54187/jnrs.1198582.
Vancouver 1.Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS [Internet]. 2022 Dec. 1;11(3):233-46. Available from: https://izlik.org/JA43ZA53ZN


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