Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Sayı: 43, 1 - 10, 30.06.2023

Ahmet Özcan Gökay Karabacak Sevcan Bulut Aykut Or

https://doi.org/10.53570/jnt.1230368

Öz

Kaynakça

  • H. Fast, \emph{Sur la Convergence Statistique}, Colloquium Mathematicae 2 (1951) 241{--}244.
  • H. Steinhaus, \emph{Sur la Convergence Ordinaire et la Convergence Asymptotique}, Colloquium Mathematicae 2 (1951) 73{--}74.
  • T. Salat, \emph{On Statistically Convergent Sequences of Real Numbers}, Mathematica Slovaca 30 (1980) 139{--}150.
  • A. R. Freedman, J. J. Sember, \emph{Densities and Summability}, Pacific Journal of Mathematics 95 (1981) 293{--}305.
  • J. A. Fridy, \emph{On Statistical Convergence}, Analysis 5 (1985) 301--313.
  • J. S. Connor, \emph{The Statistical and Strong p-Cesaro Convergence of Sequences}, Analysis 8 (1988) 47{--}63.
  • E. Kolk, \emph{Matrix Summability of Statistically Convergent Sequences}, Analysis 13 (1993) 77{--}83.
  • J. A. Fridy, C. Orhan, \emph{Lacunary Statistical Convergence}, Pacific Journal of Mathematics 160 (1993) 43{--}51.
  • S. Bulut, A. Or, \emph{$\mathcal{I}$-Statistical Rough Convergence of Order $\alpha$}, Journal of New Theory (38) (2022) 34{--}41.
  • A. Pringsheim, \emph{Zur Ttheorie der Zweifach Unendlichen Zahlenfolgen}, Mathematische Annalen 53 (1900) 289{--}321.
  • M. Mursaleen, O. H. H. Edely, \emph{Statistical Convergence of Double Sequences}, Journal of Mathematical Analysis and Applications 288 (2003) 223{--}231.
  • L. A. Zadeh, \emph{Fuzzy Sets}, Information and Control 8 (1965) 338{--}353.
  • J. Kramosil, J. Michalek, \emph{Fuzzy Metric and Statistical Metric Spaces}, Kybernetika 11 (1975) 336{--}334.
  • O. Kaleva, S. Seikkala, \emph{On Fuzzy Metric Spaces}, Fuzzy Sets and Systems 12 (1984) 215{--}229.
  • A. George, P. Veeramani, \emph{On Some Results in Fuzzy Metric Spaces}, Fuzzy Sets and Systems 64 (1994) 395{--}399.
  • D. Mihet, \emph{On Fuzzy Contractive Mappings in Fuzzy Metric Spaces}, Fuzzy Sets and Systems 158 (2007) 915{--}921.
  • V. Gregori, J. J. Mi$\check{\text{n}}$ana, S. Morillas, \emph{A Note on Convergence in Fuzzy Metric Spaces}, Iranian Journal of Fuzzy System 11 (4) (2014) 75{--}85.
  • S. Morillas, A. Sapena, \emph{On Standard Cauchy Sequences in Fuzzy Metric Spaces}, in: Proceedings of the Conference in Applied Topology WiAT'13, Bilbao, 2013, pp. 101{--}108.
  • V. Gregori, J. J. Mi$\check{\text{n}}$ana, \emph{Strong Convergence in Fuzzy Metric Spaces}, Filomat 31 (6) (2017) 1619{--}1625.
  • C. Li, Y. Zhang, J. Zhang, \emph{On Statistical Convergence in Fuzzy Metric Spaces}, Journal of Intelligent and Fuzzy Systems 39 (3) (2020) 3987{--}3993.
  • J. H. Park, \emph{Intuitionistic Fuzzy Metric Spaces}, Chaos Solitions and Fractals 22 (2004) 1039{--}1046.
  • K. T. Atanasov, \emph{Intuitionistic Fuzzy Sets}, Fuzzy Sets and Systems 20 (1) (1986) 87{--}96.
  • B. Schweizer, A. Sklar, \emph{Statistical Metric Spaces}, Pacific Journal of Mathematics 10 (1) (1960) 314--334.
  • B. P. Varol, \emph{Statistical Convergent Sequences in Intuitionistic Fuzzy Metric Spaces}, Axioms 11 (2022) 159.
  • R. Sava\c{s}, \emph{On Double Statistical Convergence in Fuzzy Metric Spaces}, in: 8th International Conference on Recent Advances in Pure and Applied Mathematics ICRAPAM, Muğla, 2021, pp. 234{--}243.

Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces

Yıl 2023, Sayı: 43, 1 - 10, 30.06.2023

Ahmet Özcan Gökay Karabacak Sevcan Bulut Aykut Or

https://doi.org/10.53570/jnt.1230368

Öz

Statistical convergence has been a prominent research area in mathematics since this concept was independently introduced by Fast and Steinhaus in 1951. Afterward, the statistical convergence of double sequences in metric spaces and fuzzy metric spaces has been widely studied. The main goal of the present study is to introduce the concepts of statistical convergence and statistical Cauchy for double sequences in intuitionistic fuzzy metric spaces. Moreover, this study characterizes the statistical convergence of a double sequence by an ordinary convergent of a subsequence of the double sequence. Besides, the current study theoretically contributes to the mentioned concepts and investigates some of their basic properties. Finally, the paper handles whether the aspects should be further investigated.

Anahtar Kelimeler

statistical convergence statistical Cauchy sequences double sequences intuitionistic fuzzy metric spaces

Kaynakça

  • H. Fast, \emph{Sur la Convergence Statistique}, Colloquium Mathematicae 2 (1951) 241{--}244.
  • H. Steinhaus, \emph{Sur la Convergence Ordinaire et la Convergence Asymptotique}, Colloquium Mathematicae 2 (1951) 73{--}74.
  • T. Salat, \emph{On Statistically Convergent Sequences of Real Numbers}, Mathematica Slovaca 30 (1980) 139{--}150.
  • A. R. Freedman, J. J. Sember, \emph{Densities and Summability}, Pacific Journal of Mathematics 95 (1981) 293{--}305.
  • J. A. Fridy, \emph{On Statistical Convergence}, Analysis 5 (1985) 301--313.
  • J. S. Connor, \emph{The Statistical and Strong p-Cesaro Convergence of Sequences}, Analysis 8 (1988) 47{--}63.
  • E. Kolk, \emph{Matrix Summability of Statistically Convergent Sequences}, Analysis 13 (1993) 77{--}83.
  • J. A. Fridy, C. Orhan, \emph{Lacunary Statistical Convergence}, Pacific Journal of Mathematics 160 (1993) 43{--}51.
  • S. Bulut, A. Or, \emph{$\mathcal{I}$-Statistical Rough Convergence of Order $\alpha$}, Journal of New Theory (38) (2022) 34{--}41.
  • A. Pringsheim, \emph{Zur Ttheorie der Zweifach Unendlichen Zahlenfolgen}, Mathematische Annalen 53 (1900) 289{--}321.
  • M. Mursaleen, O. H. H. Edely, \emph{Statistical Convergence of Double Sequences}, Journal of Mathematical Analysis and Applications 288 (2003) 223{--}231.
  • L. A. Zadeh, \emph{Fuzzy Sets}, Information and Control 8 (1965) 338{--}353.
  • J. Kramosil, J. Michalek, \emph{Fuzzy Metric and Statistical Metric Spaces}, Kybernetika 11 (1975) 336{--}334.
  • O. Kaleva, S. Seikkala, \emph{On Fuzzy Metric Spaces}, Fuzzy Sets and Systems 12 (1984) 215{--}229.
  • A. George, P. Veeramani, \emph{On Some Results in Fuzzy Metric Spaces}, Fuzzy Sets and Systems 64 (1994) 395{--}399.
  • D. Mihet, \emph{On Fuzzy Contractive Mappings in Fuzzy Metric Spaces}, Fuzzy Sets and Systems 158 (2007) 915{--}921.
  • V. Gregori, J. J. Mi$\check{\text{n}}$ana, S. Morillas, \emph{A Note on Convergence in Fuzzy Metric Spaces}, Iranian Journal of Fuzzy System 11 (4) (2014) 75{--}85.
  • S. Morillas, A. Sapena, \emph{On Standard Cauchy Sequences in Fuzzy Metric Spaces}, in: Proceedings of the Conference in Applied Topology WiAT'13, Bilbao, 2013, pp. 101{--}108.
  • V. Gregori, J. J. Mi$\check{\text{n}}$ana, \emph{Strong Convergence in Fuzzy Metric Spaces}, Filomat 31 (6) (2017) 1619{--}1625.
  • C. Li, Y. Zhang, J. Zhang, \emph{On Statistical Convergence in Fuzzy Metric Spaces}, Journal of Intelligent and Fuzzy Systems 39 (3) (2020) 3987{--}3993.
  • J. H. Park, \emph{Intuitionistic Fuzzy Metric Spaces}, Chaos Solitions and Fractals 22 (2004) 1039{--}1046.
  • K. T. Atanasov, \emph{Intuitionistic Fuzzy Sets}, Fuzzy Sets and Systems 20 (1) (1986) 87{--}96.
  • B. Schweizer, A. Sklar, \emph{Statistical Metric Spaces}, Pacific Journal of Mathematics 10 (1) (1960) 314--334.
  • B. P. Varol, \emph{Statistical Convergent Sequences in Intuitionistic Fuzzy Metric Spaces}, Axioms 11 (2022) 159.
  • R. Sava\c{s}, \emph{On Double Statistical Convergence in Fuzzy Metric Spaces}, in: 8th International Conference on Recent Advances in Pure and Applied Mathematics ICRAPAM, Muğla, 2021, pp. 234{--}243.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Ahmet Özcan 0000-0003-1458-9015

Gökay Karabacak 0000-0001-7546-8247

Sevcan Bulut 0000-0002-2926-8217

Aykut Or 0000-0001-5279-0057

Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 6 Ocak 2023
Yayımlandığı Sayı Yıl 2023 Sayı: 43

Kaynak Göster

APA Özcan, A., Karabacak, G., Bulut, S., Or, A. (2023). Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces. Journal of New Theory(43), 1-10. https://doi.org/10.53570/jnt.1230368
AMA Özcan A, Karabacak G, Bulut S, Or A. Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces. JNT. Haziran 2023;(43):1-10. doi:10.53570/jnt.1230368
Chicago Özcan, Ahmet, Gökay Karabacak, Sevcan Bulut, ve Aykut Or. “Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces”. Journal of New Theory, sy. 43 (Haziran 2023): 1-10. https://doi.org/10.53570/jnt.1230368.
EndNote Özcan A, Karabacak G, Bulut S, Or A (01 Haziran 2023) Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces. Journal of New Theory 43 1–10.
IEEE A. Özcan, G. Karabacak, S. Bulut, ve A. Or, “Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces”, JNT, sy. 43, ss. 1–10, Haziran 2023, doi: 10.53570/jnt.1230368.
ISNAD Özcan, Ahmet vd. “Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces”. Journal of New Theory 43 (Haziran 2023), 1-10. https://doi.org/10.53570/jnt.1230368.
JAMA Özcan A, Karabacak G, Bulut S, Or A. Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces. JNT. 2023;:1–10.
MLA Özcan, Ahmet vd. “Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces”. Journal of New Theory, sy. 43, 2023, ss. 1-10, doi:10.53570/jnt.1230368.
Vancouver Özcan A, Karabacak G, Bulut S, Or A. Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces. JNT. 2023(43):1-10.
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