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On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces

Yıl 2022, , 35 - 45, 17.03.2022

Ömer Kişi , Verda Gürdal

https://doi.org/10.33434/cams.1025928
Cited By: 3

Öz

The aim of this article is to investigate triple $\Delta $-statistical convergent sequences in a neutrosophic normed space (NNS). Also, we examine the notions of $\Delta $-statistical limit points and $\Delta $-statistical cluster points and prove their important features.

Anahtar Kelimeler

Difference sequence Lacunary sequence Neutrosophic normed space Triple sequence

Kaynakça

  • [1] L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
  • [2] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046.
  • [3] F. Lael, K. Nourouzi, Some results on the IF-normed spaces, Chaos Solitons Fractals, 37 (2008), 931-939.
  • [4] S. Karakuş, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763-769.
  • [5] S. Karakuş, K. Demirci, Ş. Yardımcı, Statistical limit points of sequences on intuitionistic fuzzy normed spaces, J. Concr. Appl. Math., 6(4) (2008), 375-386.
  • [6] P. Debnath, A generalised statistical convergence in intuitionistic fuzzy n-normed linear spaces, Ann. Fuzzy Math. Inform., 12(4) (2016) 559-572.
  • [7] E. Savas¸, M. G¨urdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41 (2015), 289-294.
  • [8] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24(3) (2005), 287-297.
  • [9] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 1998.
  • [10] M. Kirişci, N. Şimşek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241-248.
  • [11] M. Kirişci, N. Şimşek, Neutrosophic normed spaces and statistical convergence, J. Anal., 28 (2020), 1059-1073.
  • [12] M. Kirişci, N. Şimşek, M. Akyiğit, Fixed point results for a new metric space, Math. Methods Appl. Sci., 44(9) (2020), 7416-7422.
  • [13] Ö. Kişi, Lacunary statistical convergence of sequences in neutrosophic normed spaces, 4th International Conference on Mathematics: An Istanbul Meeting for World Mathematicians, Istanbul, 345-354, 2020.
  • [14] Ö. Kişi, Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2) (2021), 2581-2590.
  • [15] V. A. Khan, M. D. Khan, M. Ahmad, Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets Syst., 42 (2021), 239-252.
  • [16] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
  • [17] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [18] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.
  • [19] A. A. Nabiev, E. Savaş, M. Gürdal, Statistically localized sequences in metric spaces, J. Appl. Anal. Comput., 9(2) (2019), 739-746.
  • [20] E. Savaş, M. Gürdal, Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Systems., 27(4) (2014), 2067-2075.
  • [21] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223-231.
  • [22] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
  • [23] A. Şahiner, M. Gürdal, F. K. Düden, Triple sequences and their statistical convergence, Selc¸uk J. Appl. Math., 8(2) (2007), 49-55.
  • [24] A. Esi, Statistical convergence of triple sequences in topological groups, Annals Univ. Craiova. math. Comput. Sci. Ser., 10(1) (2013), 29-33.
  • [25] B. C. Tripathy, R. Goswami, On triple difference sequences of real numbers in propobabilistic normed space, Proyecciones J. Math., 33(2) (2014), 157-174.
  • [26] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169-176.
  • [27] M. Başarır, On the statistical convergence of sequences, Fırat Univ. Turk. J. Sci. Technol., 2 (1995), 1-6.
  • [28] R. Çolak, H. Altınok, M. Et, Generalized difference sequences of fuzzy numbers, Chaos Solitons Fractals, 40(3) (2009), 1106-1117.
  • [29] Y. Altın, M. Bas¸arır, M. Et, On some generalized difference sequences of fuzzy numbers, Kuwait J. Sci., 34(1A) (2007), 1-14.
  • [30] S. Altundağ, E. Kamber, Lacunary D-statistical convergence in intuitionistic fuzzy n-normed space, J. Inequal. Appl., 2014(40) (2014), 1-12.
  • [31] B. Hazarika, A. Alotaibi, S.A. Mohiudine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24(9) (2020), 6613-6622.
  • [32] F. Başar, Summability theory and its applications, Bentham Science Publishers, Istanbul, 2012.
  • [33] M. Mursaleen, F. Başar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its Applications, Boca Raton London New York, 2020.
  • [34] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA, 28(12) (1942), 535-537.

Yıl 2022, , 35 - 45, 17.03.2022

Ömer Kişi , Verda Gürdal

https://doi.org/10.33434/cams.1025928
Cited By: 3

Öz

Kaynakça

  • [1] L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
  • [2] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046.
  • [3] F. Lael, K. Nourouzi, Some results on the IF-normed spaces, Chaos Solitons Fractals, 37 (2008), 931-939.
  • [4] S. Karakuş, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763-769.
  • [5] S. Karakuş, K. Demirci, Ş. Yardımcı, Statistical limit points of sequences on intuitionistic fuzzy normed spaces, J. Concr. Appl. Math., 6(4) (2008), 375-386.
  • [6] P. Debnath, A generalised statistical convergence in intuitionistic fuzzy n-normed linear spaces, Ann. Fuzzy Math. Inform., 12(4) (2016) 559-572.
  • [7] E. Savas¸, M. G¨urdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41 (2015), 289-294.
  • [8] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24(3) (2005), 287-297.
  • [9] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 1998.
  • [10] M. Kirişci, N. Şimşek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241-248.
  • [11] M. Kirişci, N. Şimşek, Neutrosophic normed spaces and statistical convergence, J. Anal., 28 (2020), 1059-1073.
  • [12] M. Kirişci, N. Şimşek, M. Akyiğit, Fixed point results for a new metric space, Math. Methods Appl. Sci., 44(9) (2020), 7416-7422.
  • [13] Ö. Kişi, Lacunary statistical convergence of sequences in neutrosophic normed spaces, 4th International Conference on Mathematics: An Istanbul Meeting for World Mathematicians, Istanbul, 345-354, 2020.
  • [14] Ö. Kişi, Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2) (2021), 2581-2590.
  • [15] V. A. Khan, M. D. Khan, M. Ahmad, Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets Syst., 42 (2021), 239-252.
  • [16] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
  • [17] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [18] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.
  • [19] A. A. Nabiev, E. Savaş, M. Gürdal, Statistically localized sequences in metric spaces, J. Appl. Anal. Comput., 9(2) (2019), 739-746.
  • [20] E. Savaş, M. Gürdal, Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Systems., 27(4) (2014), 2067-2075.
  • [21] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223-231.
  • [22] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
  • [23] A. Şahiner, M. Gürdal, F. K. Düden, Triple sequences and their statistical convergence, Selc¸uk J. Appl. Math., 8(2) (2007), 49-55.
  • [24] A. Esi, Statistical convergence of triple sequences in topological groups, Annals Univ. Craiova. math. Comput. Sci. Ser., 10(1) (2013), 29-33.
  • [25] B. C. Tripathy, R. Goswami, On triple difference sequences of real numbers in propobabilistic normed space, Proyecciones J. Math., 33(2) (2014), 157-174.
  • [26] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169-176.
  • [27] M. Başarır, On the statistical convergence of sequences, Fırat Univ. Turk. J. Sci. Technol., 2 (1995), 1-6.
  • [28] R. Çolak, H. Altınok, M. Et, Generalized difference sequences of fuzzy numbers, Chaos Solitons Fractals, 40(3) (2009), 1106-1117.
  • [29] Y. Altın, M. Bas¸arır, M. Et, On some generalized difference sequences of fuzzy numbers, Kuwait J. Sci., 34(1A) (2007), 1-14.
  • [30] S. Altundağ, E. Kamber, Lacunary D-statistical convergence in intuitionistic fuzzy n-normed space, J. Inequal. Appl., 2014(40) (2014), 1-12.
  • [31] B. Hazarika, A. Alotaibi, S.A. Mohiudine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24(9) (2020), 6613-6622.
  • [32] F. Başar, Summability theory and its applications, Bentham Science Publishers, Istanbul, 2012.
  • [33] M. Mursaleen, F. Başar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its Applications, Boca Raton London New York, 2020.
  • [34] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA, 28(12) (1942), 535-537.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ömer Kişi 0000-0001-6844-3092

Verda Gürdal 0000-0001-5130-7844

Yayımlanma Tarihi 17 Mart 2022
Gönderilme Tarihi 19 Kasım 2021
Kabul Tarihi 21 Aralık 2021
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Kişi, Ö., & Gürdal, V. (2022). On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces. Communications in Advanced Mathematical Sciences, 5(1), 35-45. https://doi.org/10.33434/cams.1025928
AMA Kişi Ö, Gürdal V. On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces. Communications in Advanced Mathematical Sciences. Mart 2022;5(1):35-45. doi:10.33434/cams.1025928
Chicago Kişi, Ömer, ve Verda Gürdal. “On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces”. Communications in Advanced Mathematical Sciences 5, sy. 1 (Mart 2022): 35-45. https://doi.org/10.33434/cams.1025928.
EndNote Kişi Ö, Gürdal V (01 Mart 2022) On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces. Communications in Advanced Mathematical Sciences 5 1 35–45.
IEEE Ö. Kişi ve V. Gürdal, “On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces”, Communications in Advanced Mathematical Sciences, c. 5, sy. 1, ss. 35–45, 2022, doi: 10.33434/cams.1025928.
ISNAD Kişi, Ömer - Gürdal, Verda. “On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces”. Communications in Advanced Mathematical Sciences 5/1 (Mart 2022), 35-45. https://doi.org/10.33434/cams.1025928.
JAMA Kişi Ö, Gürdal V. On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces. Communications in Advanced Mathematical Sciences. 2022;5:35–45.
MLA Kişi, Ömer ve Verda Gürdal. “On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces”. Communications in Advanced Mathematical Sciences, c. 5, sy. 1, 2022, ss. 35-45, doi:10.33434/cams.1025928.
Vancouver Kişi Ö, Gürdal V. On Triple Difference Sequences of Real Numbers in Neutrosophic Normed Spaces. Communications in Advanced Mathematical Sciences. 2022;5(1):35-4.

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https://doi.org/10.2298/FIL2319443A
Hibrid Δ-Statistical Convergence for Neutrosophic Normed Space
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https://doi.org/10.1155/2022/3890308

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