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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

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

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 Articles
Authors

Ahmet Özcan 0000-0003-1458-9015

Aykut Or 0000-0001-5279-0057

Publication Date December 31, 2022
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 Özcan A, Or A. Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces. JNRS. December 2022;11(3):233-246. doi:10.54187/jnrs.1198582
Chicago Özcan, Ahmet, and Aykut Or. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science 11, no. 3 (December 2022): 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 A. Özcan and A. Or, “Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces”, JNRS, vol. 11, no. 3, pp. 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 (December 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 and Aykut Or. “Rough Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Spaces”. Journal of New Results in Science, vol. 11, no. 3, 2022, pp. 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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