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Year 2020, Volume: 3 Issue: 2, 101 - 108, 15.12.2020
https://doi.org/10.33401/fujma.792994

Abstract

References

  • [1] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, In VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal of Bioautomation 2016; 20(S1): S1-S6 (in English).
  • [3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96.
  • [4] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039–1046.
  • [5] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331–344.
  • [6] F. Lael, K. Nourouzi, Some results on the IF􀀀normed spaces, Chaos Solitons Fractals, 37 (2008), 931–939.
  • [7] S. Karakus, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763–769.
  • [8] M. Mursaleen, S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233 (2009), 142–149.
  • [9] M. Mursaleen, S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 41 (2009), 2414–2421.
  • [10] S. A. Mohiuddine, Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals, 42 (2009), 1731–1737.
  • [11] M. Mursaleen, S. A. Mohiuddine, H. H. E. Osama, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603–611.
  • [12] Ö. Talo, E. Yavuz, Cesa`ro summability of sequences in intuitionistic fuzzy normed spaces and related Tauberian theorems, Soft Comput., (2020), doi: 10.1007/s00500-020-05301-z.
  • [13] H. Efe, C. Alaca, Compact and bounded sets in intuitionistic fuzzy metric spaces, Demonstr. Math., 40(2) (2007), 449–456.
  • [14] E. Yavuz, H. Çoşkun, On the logarithmic summability method for sequences of fuzzy numbers, Soft Comput., 21 (2017), 5779–5785.
  • [15] E. Yavuz, Tauberian theorems for statistical summability methods of sequences of fuzzy numbers, Soft Comput., 23 (2019), 5659–5665.
  • [16] S. A. Sezer, Logarithmic means of sequences of fuzzy numbers and a Tauberian theorem, Soft Comput., 24 (2020), 367–374.
  • [17] S. A. Sezer, Statistical harmonic summability of sequences of fuzzy numbers, Soft Comput., (2020), doi: 10.1007/s00500-020-05151-9.
  • [18] E. Dündar, Ö. Talo, F. Başar, Regularly (I2;I)􀀀convergence and regularly (I2;I)􀀀Cauchy double sequences of fuzzy numbers, International Journal of Analysis, (2013), Article ID 749684, 7 pages.
  • [19] E. Dündar, Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst., 10(3) (2013), 37–50.
  • [20] M. R. Türkmen, E. Dündar, U. Ulusu, Fuzzy n-normlu uzaylarda c¸ift dizilerin Lacunary ideal yakınsaklı˘gı, International Congresson Science and Education (ICSE 2018), Afyonkarahisar, Turkey, 2018.
  • [21] U. Ulusu, E. Dündar, Asymptotically I-Ces`aro equivalence of sequences of sets, Univers. J. Math. Appl., 1(2) (2018), 101–105.
  • [22] M. R. T¨urkmen, E. Dündar, On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, J. Intell. Fuzzy Syst., 36(2) (2019), 1683–1690.
  • [23] E. Dündar, M. R. Türkmen, On I2-convergence and I-2 -convergence of double sequences in fuzzy normed spaces, Konuralp J. Math., 7(2) (2019), 405–409.
  • [24] E. Dündar, M. R. Türkmen, On I2-Cauchy double sequences in fuzzy normed spaces, Commun. Adv. Math. Sci., 2(2) (2019), 154–160.
  • [25] E. Dündar, M. R. Türkmen, N. P. Akın, Regularly ideal convergence of double sequences in fuzzy normed spaces, Bull. Math. Anal. Appl., 12(2) (2020), 12–26.
  • [26] Ü. Totur, İ. Çanak, Tauberian theorems for (¯N; p;q) summable double sequences of fuzzy numbers, Soft Comput., 24 (2020), 2301–2310.
  • [27] F. Moricz, Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences, Studia Math., 219 (2013), 109–121.
  • [28] F. Moricz, On the harmonic averages of numerical sequences, Arch. Math. (Basel), 86 (2006), 375–384.

On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces

Year 2020, Volume: 3 Issue: 2, 101 - 108, 15.12.2020
https://doi.org/10.33401/fujma.792994

Abstract

We introduce logarithmic summability in intuitionistic fuzzy normed spaces($IFNS$) and give some Tauberian conditions for which logarithmic summability yields convergence in $IFNS$. Besides, we define the concept of slow oscillation with respect to logarithmic summability in $IFNS$, investigate its relation with the concept of q-boundedness and give Tauberian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between Ces\`{a}ro summability method and logarithmic summability method in $IFNS$ is also proved in the paper.

References

  • [1] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, In VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal of Bioautomation 2016; 20(S1): S1-S6 (in English).
  • [3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96.
  • [4] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039–1046.
  • [5] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331–344.
  • [6] F. Lael, K. Nourouzi, Some results on the IF􀀀normed spaces, Chaos Solitons Fractals, 37 (2008), 931–939.
  • [7] S. Karakus, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35 (2008), 763–769.
  • [8] M. Mursaleen, S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233 (2009), 142–149.
  • [9] M. Mursaleen, S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 41 (2009), 2414–2421.
  • [10] S. A. Mohiuddine, Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals, 42 (2009), 1731–1737.
  • [11] M. Mursaleen, S. A. Mohiuddine, H. H. E. Osama, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603–611.
  • [12] Ö. Talo, E. Yavuz, Cesa`ro summability of sequences in intuitionistic fuzzy normed spaces and related Tauberian theorems, Soft Comput., (2020), doi: 10.1007/s00500-020-05301-z.
  • [13] H. Efe, C. Alaca, Compact and bounded sets in intuitionistic fuzzy metric spaces, Demonstr. Math., 40(2) (2007), 449–456.
  • [14] E. Yavuz, H. Çoşkun, On the logarithmic summability method for sequences of fuzzy numbers, Soft Comput., 21 (2017), 5779–5785.
  • [15] E. Yavuz, Tauberian theorems for statistical summability methods of sequences of fuzzy numbers, Soft Comput., 23 (2019), 5659–5665.
  • [16] S. A. Sezer, Logarithmic means of sequences of fuzzy numbers and a Tauberian theorem, Soft Comput., 24 (2020), 367–374.
  • [17] S. A. Sezer, Statistical harmonic summability of sequences of fuzzy numbers, Soft Comput., (2020), doi: 10.1007/s00500-020-05151-9.
  • [18] E. Dündar, Ö. Talo, F. Başar, Regularly (I2;I)􀀀convergence and regularly (I2;I)􀀀Cauchy double sequences of fuzzy numbers, International Journal of Analysis, (2013), Article ID 749684, 7 pages.
  • [19] E. Dündar, Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst., 10(3) (2013), 37–50.
  • [20] M. R. Türkmen, E. Dündar, U. Ulusu, Fuzzy n-normlu uzaylarda c¸ift dizilerin Lacunary ideal yakınsaklı˘gı, International Congresson Science and Education (ICSE 2018), Afyonkarahisar, Turkey, 2018.
  • [21] U. Ulusu, E. Dündar, Asymptotically I-Ces`aro equivalence of sequences of sets, Univers. J. Math. Appl., 1(2) (2018), 101–105.
  • [22] M. R. T¨urkmen, E. Dündar, On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, J. Intell. Fuzzy Syst., 36(2) (2019), 1683–1690.
  • [23] E. Dündar, M. R. Türkmen, On I2-convergence and I-2 -convergence of double sequences in fuzzy normed spaces, Konuralp J. Math., 7(2) (2019), 405–409.
  • [24] E. Dündar, M. R. Türkmen, On I2-Cauchy double sequences in fuzzy normed spaces, Commun. Adv. Math. Sci., 2(2) (2019), 154–160.
  • [25] E. Dündar, M. R. Türkmen, N. P. Akın, Regularly ideal convergence of double sequences in fuzzy normed spaces, Bull. Math. Anal. Appl., 12(2) (2020), 12–26.
  • [26] Ü. Totur, İ. Çanak, Tauberian theorems for (¯N; p;q) summable double sequences of fuzzy numbers, Soft Comput., 24 (2020), 2301–2310.
  • [27] F. Moricz, Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences, Studia Math., 219 (2013), 109–121.
  • [28] F. Moricz, On the harmonic averages of numerical sequences, Arch. Math. (Basel), 86 (2006), 375–384.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Enes Yavuz 0000-0002-4335-5210

Publication Date December 15, 2020
Submission Date September 10, 2020
Acceptance Date November 16, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Yavuz, E. (2020). On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces. Fundamental Journal of Mathematics and Applications, 3(2), 101-108. https://doi.org/10.33401/fujma.792994
AMA Yavuz E. On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces. Fundam. J. Math. Appl. December 2020;3(2):101-108. doi:10.33401/fujma.792994
Chicago Yavuz, Enes. “On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces”. Fundamental Journal of Mathematics and Applications 3, no. 2 (December 2020): 101-8. https://doi.org/10.33401/fujma.792994.
EndNote Yavuz E (December 1, 2020) On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces. Fundamental Journal of Mathematics and Applications 3 2 101–108.
IEEE E. Yavuz, “On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces”, Fundam. J. Math. Appl., vol. 3, no. 2, pp. 101–108, 2020, doi: 10.33401/fujma.792994.
ISNAD Yavuz, Enes. “On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces”. Fundamental Journal of Mathematics and Applications 3/2 (December 2020), 101-108. https://doi.org/10.33401/fujma.792994.
JAMA Yavuz E. On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces. Fundam. J. Math. Appl. 2020;3:101–108.
MLA Yavuz, Enes. “On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces”. Fundamental Journal of Mathematics and Applications, vol. 3, no. 2, 2020, pp. 101-8, doi:10.33401/fujma.792994.
Vancouver Yavuz E. On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces. Fundam. J. Math. Appl. 2020;3(2):101-8.

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