Research Article
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Year 2021, Volume: 4 Issue: 2, 67 - 76, 01.06.2021

Ömer Kişi

https://doi.org/10.33401/fujma.873029
https://izlik.org/JA39HG42EC

Abstract

References

  • [1] L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
  • [2] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Syst., 20 (1986), 87-96.
  • [3] K.T. Atanassov, G. Pasi, R. Yager, Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, Proceedings of First International IEEE Symposium Intelligent Systems, 1 (2002), 115-119.
  • [4] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
  • [5] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst., 12 (1984), 215-229.
  • [6] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399.
  • [7] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Syst., 90 (1997), 365-368.
  • [8] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046.
  • [9] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331-344.
  • [10] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [11] S. Karaku¸s, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763-769.
  • [12] M. Kiri¸sci, Fibonacci statistical convergence on intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 36 (2019), 5597-5604.
  • [13] S.A. Mohiuddine, Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals, 42 (2009), 1731-1737.
  • [14] E. Savaş, M. Gürdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 27(4) (2014), 1621-1629.
  • [15] E. Savaş, M. Gürdal, Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Systems, 27(4) (2014), 2067-2075.
  • [16] E. Savaş, M. Gürdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41 (2015), 289-294.
  • [17] E. Yavuz, On the logarithmic summability of sequences in intuitionistic fuzzy normed spaces, Fundam. J. Math. Appl., 3(2) (2020), 101-108.
  • [18] J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pac. J. Math., 160(1) (1993), 43-51.
  • [19] J.A. Fridy, C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173(2) (1993), 497-504.
  • [20] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Syst., 99(3) (1998), 353-355.
  • [21] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715.
  • [22] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., (2013), Article ID 868457, 8 pages.
  • [23] M. Mursaleen, S.A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233(2) (2009), 142-149.
  • [24] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24 (2005), 287-297.
  • [25] F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA (1998).
  • [26] T. Bera, N.K. Mahapatra, On neutrosophic soft linear spaces, Fuzzy Inform. Engineering, 9 (3) (2017), 299-324.
  • [27] T. Bera, N.K. Mahapatra, Neutrosophic soft normed linear spaces, Neutrosophic Sets and Systems, 23 (2018), 52-71.
  • [28] T. Bera, N.K. Mahapatra, On neutrosophic soft metric space, Int. J. Adv. Math., 2018(1) (2018), 180-200.
  • [29] T. Bera, N.K. Mahapatra, Compactness and Continuity on Neutrosophic Soft Metric Space, Int. J. Adv. Math., 2018(4) (2018), 1-24.
  • [30] T. Bera, N. K. Mahapatra, Continuity and Convergence on neutrosophic soft normed linear spaces, Int. J. Fuzzy Comput. Modelling, 3(2) (2020), 156-186.
  • [31] T.K. Samanta, Iqbal H. Jebril, Finite dimensional intuitionistic fuzzy normed linear space, Int. J. Open Problems Compt. Math., 2(4) (2009), 574-591.
  • [32] T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear spaces, Ann. Fuzzy Math. Inform., 6(2) (2013), 271-283.
  • [33] M. Kirisci, N. Şimşek, Neutrosophic metric spaces, Math. Sci, 14 (2020), 241-248.
  • [34] M. Kirisci, N. Şimşek, Neutrosophic normed spaces and statistical convergence, The Journal of Analysis, 28 (2020), 1059-1073.
  • [35] F. Smarandache, A unifying field in logics: Neutrosophic logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan (2003).
  • [36] F. Smarandache, Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability, Sitech-Education, Columbus, Craiova, (2013), 1-143.
  • [37] N. Şimşek, M. Kirişci, Fixed point theorems in neutrosophic metric spaces, Sigma J. Eng. Nat. Sci., 10(2) (2019), 221-230.
  • [38] M. Kirisci, N. Şimşek, M. Akyiğit, Fixed point results for a new metric space, Math. Meth. Appl. Sci., 2020 1-7. doi: 10.1002/mma.6189.
  • [39] Ö. Ki¸si, Lacunary statistical convergence of sequences in neutrosophic normed spaces, 4th International Conference on Mathematics: An Istanbul Meeting for World Mathematicians, Istanbul, 2020, 345-354.
  • [40] P. Kostyrko, T. Salát and W. Wilczynsski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • [41] P. Kostyrko, M. Macaj, T. Salát, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443-464.
  • [42] A. A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569-566.
  • [43] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math., 4(1) (2012), 85-91.
  • [44] U. Yamancı, M. Gürdal, I-statistical convergence in 2-normed space, Arab J. Math. Sci., 20(1) (2014), 41-47.
  • 45] U. Yamancı, M. Gürdal, I-statistically preCauchy double sequences, Glob. J. Math. Anal., 2(4) (2014), 297-303.
  • [46] E. Dündar, M. R. Türkmen, On I2-Cauchy double sequences in fuzzy normed spaces, Commun. Adv. Math. Sci., 2(2) (2019), 154-160.
  • [47] Ö. Ki¸si, E. Güler, I-Cesáro Summability of a Sequence of Order a of Random Variables in Probability, Fundam. J. Math. Appl., 1(2) (2018), 157-161.
  • [48] S. A. Mohiuddine, B. Hazarika, M. A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560.
  • [49] S. A. Mohiuddine, B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat, 31(6) (2017), 1827-1834.
  • [50] K. Raj, S. A. Mohiuddine, Applications of lacunary sequences to develop fuzzy sequence spaces for ideal convergence and orlicz function, Eur. J. Pure Appl. Math., 13(5) (2020), 1131-1148.
  • [51] V.A. Khan, S.A.A. Abdulla, K.M.A.S. Alshlool, Paranorm ideal convergent fibonacci difference sequence spaces, Commun. Adv. Math. Sci., 2(4) (2019), 293-302.
  • [52] M. Mursaleen, S.A. Mohiuddine, O.H.H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603-611.
  • [53] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci., 28(12) (1942), 535-537.

On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces

Year 2021, Volume: 4 Issue: 2, 67 - 76, 01.06.2021

Ömer Kişi

https://doi.org/10.33401/fujma.873029
https://izlik.org/JA39HG42EC

Abstract

The purpose of this article is to investigate lacunary ideal convergence of sequences in neutrosophic normed space (NNS). Also, an original notion, named lacunary convergence of sequence in NNS, is defined. Also, lacunary $% \mathcal{I}$-limit points and lacunary $\mathcal{I}$-cluster points of sequences in NNS have been examined. Furthermore, lacunary Cauchy and lacunary $\mathcal{I}$-Cauchy sequences in NNS are introduced and some properties of these notions are studied.

Keywords

Lacunary ideal convergence Lacunary convergence Lacunary $% \mathcal{I}$-limit points Lacunary $\mathcal{I}$-cluster points Neutrosophic normed space

References

  • [1] L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
  • [2] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Syst., 20 (1986), 87-96.
  • [3] K.T. Atanassov, G. Pasi, R. Yager, Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, Proceedings of First International IEEE Symposium Intelligent Systems, 1 (2002), 115-119.
  • [4] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
  • [5] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst., 12 (1984), 215-229.
  • [6] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399.
  • [7] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Syst., 90 (1997), 365-368.
  • [8] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046.
  • [9] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331-344.
  • [10] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [11] S. Karaku¸s, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763-769.
  • [12] M. Kiri¸sci, Fibonacci statistical convergence on intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 36 (2019), 5597-5604.
  • [13] S.A. Mohiuddine, Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals, 42 (2009), 1731-1737.
  • [14] E. Savaş, M. Gürdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 27(4) (2014), 1621-1629.
  • [15] E. Savaş, M. Gürdal, Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Systems, 27(4) (2014), 2067-2075.
  • [16] E. Savaş, M. Gürdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41 (2015), 289-294.
  • [17] E. Yavuz, On the logarithmic summability of sequences in intuitionistic fuzzy normed spaces, Fundam. J. Math. Appl., 3(2) (2020), 101-108.
  • [18] J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pac. J. Math., 160(1) (1993), 43-51.
  • [19] J.A. Fridy, C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173(2) (1993), 497-504.
  • [20] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Syst., 99(3) (1998), 353-355.
  • [21] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715.
  • [22] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., (2013), Article ID 868457, 8 pages.
  • [23] M. Mursaleen, S.A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233(2) (2009), 142-149.
  • [24] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24 (2005), 287-297.
  • [25] F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA (1998).
  • [26] T. Bera, N.K. Mahapatra, On neutrosophic soft linear spaces, Fuzzy Inform. Engineering, 9 (3) (2017), 299-324.
  • [27] T. Bera, N.K. Mahapatra, Neutrosophic soft normed linear spaces, Neutrosophic Sets and Systems, 23 (2018), 52-71.
  • [28] T. Bera, N.K. Mahapatra, On neutrosophic soft metric space, Int. J. Adv. Math., 2018(1) (2018), 180-200.
  • [29] T. Bera, N.K. Mahapatra, Compactness and Continuity on Neutrosophic Soft Metric Space, Int. J. Adv. Math., 2018(4) (2018), 1-24.
  • [30] T. Bera, N. K. Mahapatra, Continuity and Convergence on neutrosophic soft normed linear spaces, Int. J. Fuzzy Comput. Modelling, 3(2) (2020), 156-186.
  • [31] T.K. Samanta, Iqbal H. Jebril, Finite dimensional intuitionistic fuzzy normed linear space, Int. J. Open Problems Compt. Math., 2(4) (2009), 574-591.
  • [32] T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear spaces, Ann. Fuzzy Math. Inform., 6(2) (2013), 271-283.
  • [33] M. Kirisci, N. Şimşek, Neutrosophic metric spaces, Math. Sci, 14 (2020), 241-248.
  • [34] M. Kirisci, N. Şimşek, Neutrosophic normed spaces and statistical convergence, The Journal of Analysis, 28 (2020), 1059-1073.
  • [35] F. Smarandache, A unifying field in logics: Neutrosophic logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan (2003).
  • [36] F. Smarandache, Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability, Sitech-Education, Columbus, Craiova, (2013), 1-143.
  • [37] N. Şimşek, M. Kirişci, Fixed point theorems in neutrosophic metric spaces, Sigma J. Eng. Nat. Sci., 10(2) (2019), 221-230.
  • [38] M. Kirisci, N. Şimşek, M. Akyiğit, Fixed point results for a new metric space, Math. Meth. Appl. Sci., 2020 1-7. doi: 10.1002/mma.6189.
  • [39] Ö. Ki¸si, Lacunary statistical convergence of sequences in neutrosophic normed spaces, 4th International Conference on Mathematics: An Istanbul Meeting for World Mathematicians, Istanbul, 2020, 345-354.
  • [40] P. Kostyrko, T. Salát and W. Wilczynsski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • [41] P. Kostyrko, M. Macaj, T. Salát, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443-464.
  • [42] A. A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569-566.
  • [43] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math., 4(1) (2012), 85-91.
  • [44] U. Yamancı, M. Gürdal, I-statistical convergence in 2-normed space, Arab J. Math. Sci., 20(1) (2014), 41-47.
  • 45] U. Yamancı, M. Gürdal, I-statistically preCauchy double sequences, Glob. J. Math. Anal., 2(4) (2014), 297-303.
  • [46] E. Dündar, M. R. Türkmen, On I2-Cauchy double sequences in fuzzy normed spaces, Commun. Adv. Math. Sci., 2(2) (2019), 154-160.
  • [47] Ö. Ki¸si, E. Güler, I-Cesáro Summability of a Sequence of Order a of Random Variables in Probability, Fundam. J. Math. Appl., 1(2) (2018), 157-161.
  • [48] S. A. Mohiuddine, B. Hazarika, M. A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560.
  • [49] S. A. Mohiuddine, B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat, 31(6) (2017), 1827-1834.
  • [50] K. Raj, S. A. Mohiuddine, Applications of lacunary sequences to develop fuzzy sequence spaces for ideal convergence and orlicz function, Eur. J. Pure Appl. Math., 13(5) (2020), 1131-1148.
  • [51] V.A. Khan, S.A.A. Abdulla, K.M.A.S. Alshlool, Paranorm ideal convergent fibonacci difference sequence spaces, Commun. Adv. Math. Sci., 2(4) (2019), 293-302.
  • [52] M. Mursaleen, S.A. Mohiuddine, O.H.H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603-611.
  • [53] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci., 28(12) (1942), 535-537.
There are 53 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ömer Kişi 0000-0001-6844-3092

Submission Date February 2, 2021
Acceptance Date April 18, 2021
Publication Date June 1, 2021
DOI https://doi.org/10.33401/fujma.873029
IZ https://izlik.org/JA39HG42EC
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Kişi, Ö. (2021). On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces. Fundamental Journal of Mathematics and Applications, 4(2), 67-76. https://doi.org/10.33401/fujma.873029
AMA 1.Kişi Ö. On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces. Fundam. J. Math. Appl. 2021;4(2):67-76. doi:10.33401/fujma.873029
Chicago Kişi, Ömer. 2021. “On $\mathcal{I}_{\theta }$-Convergence in Neutrosophic Normed Spaces”. Fundamental Journal of Mathematics and Applications 4 (2): 67-76. https://doi.org/10.33401/fujma.873029.
EndNote Kişi Ö (June 1, 2021) On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces. Fundamental Journal of Mathematics and Applications 4 2 67–76.
IEEE [1]Ö. Kişi, “On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces”, Fundam. J. Math. Appl., vol. 4, no. 2, pp. 67–76, June 2021, doi: 10.33401/fujma.873029.
ISNAD Kişi, Ömer. “On $\mathcal{I}_{\theta }$-Convergence in Neutrosophic Normed Spaces”. Fundamental Journal of Mathematics and Applications 4/2 (June 1, 2021): 67-76. https://doi.org/10.33401/fujma.873029.
JAMA 1.Kişi Ö. On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces. Fundam. J. Math. Appl. 2021;4:67–76.
MLA Kişi, Ömer. “On $\mathcal{I}_{\theta }$-Convergence in Neutrosophic Normed Spaces”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 2, June 2021, pp. 67-76, doi:10.33401/fujma.873029.
Vancouver 1.Ömer Kişi. On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces. Fundam. J. Math. Appl. 2021 Jun. 1;4(2):67-76. doi:10.33401/fujma.873029

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