International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 19 , Issue 3 , PP: 29-39, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces

M. Jeyaraman 1 * , P. Jenifer 2 , U. Praveena 3

  • 1 Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India - (jeya.math@gmail.com)
  • 2 Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India - (Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India)
  • 3 Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India - (upraveenasvg@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190303

    Received: May 03, 2021 Accepted: October 20, 2022
    Abstract

    We introduce logarithmic summability in Neutrosophic Normed Spaces [NNS] and give some Taubarian conditions for which logarithmic summability yields convergence in NNS. Besides we define the concept of slow oscillation with respect to logarithmic summability in NNS, Investigate its relation with the concept of q-boundedness and give Taubarian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability.  A comparison theorem between CesaroSummability method and logarithmic summability method in NNS is also proved in the paper.

    Keywords :

    Neutrosophic Normed Spaces , Logarithm Summability , Slow Oscillation , Taubarian Theorem.

    References

    [1] Atanassov .K, intuitionistic fuzzy sets, Fuzzy Sets Syst, 20, 87-96, (1986).

    [2] Jeyaraman, M., Mangayarkarasi, A.N., Jeyanthi, V and Pandiselvi, R., Hyers-Ulam-Rassias

    stability for functional equation in neutrosophic normed spaces, International Journal of

    Neutrosophic Science, Vol. 18, No. 1, 127-143, (2022).

    [3] Jeyaraman, M., Ramachandran, A. and Shakila, V. B.: Approximate Fixed Point Theorems For

    Weak Contractions On Neutrosophic Normed Spaces, Journal of Computational Mathematica, 6

    (1), 134-158, (2022).

    [4] Karakus .S, Denurcum .K, Duman .O, Statistical convergence on intuitionistic fuzzy normed

    spaces, Chaos Solitons Fractals, 35 763-769, (2008).

    [5] Lael .F ,Noutrouzi .K, Some results on the Intuitionistic fuzzy normed spaces, Chaos Solitons

    Fractals, 37 931-939, (2008).

    [6] Mohiuddine .S.A, DanishLohani . Q. M, On generalized statistical convergence in

    intuitionistic fuzzy normed spaces, 42 1731-1737, (2009).

    [7] Mursaleen .M, Mohiuddine. S.A., On lacunary statistical convergence with respect to the

    intuitionistic fuzzy normed space. 233, 142-149, (2009).

    [8] Mursaleen .M, Mohiuddine . S. A, Statistical convergence of double sequences in intuitionistic

    fuzzy normed spaces, Chaos Solitons Fractals, 41, 2414-2421, (2009).

    [9] Mursaleen .M, Mohiuddine . S. A, H.H.E. Osama, On the ideal convergence of double

    sequences in intuitionistic fuzzy normed spaces, 59, 603-611, (2010) .

    [10] Park . J.H. , Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 221039-1046, (2004).

    [11] Savas. E, Gurdal.M, Generalized statistically convergent sequence of functions in fuzzy 2-

    normed spaces, 27(4), 2067-2075, (2014).

    [12] Saadati . R, park . J.H, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals

    27, 331-344, (2006).

    [13] Savas .E, Gurdal .M, Certainsummability methods in intuitionistic fuzzy normed spaces, J.Intell.

    Fuzzy systems, 27 (4), 1621-1629, (2014).

    [14] Smarandache. F, Neutrosophic . Neutrosophic Probability, Set, and Logic, Pri-Quest

    Information and Learning, Ann Arbor, Michigan , USA (1998).

    [15] Simsek. N, Kirisci. M, Fixed point theorems in neutrosophic metric spaces, Sigma J Eng.

    Nat. Sci., 10(2) (2019), 221-230.

    [16] Sowndrarajan S, Jeyaraman M and Smarandache, F. Fixed Point theorems in neutrosophic

    metric spaces Neutrosophic Sets and Systems, Volume 36, 251-268, (2020).

    [17] Talo .O, Yavuz .E, Cesarosummabillity of sequence in intuitionistic fuzzy normed spaces and

    related Tauberian theorems, (2020).

    [18] Yavuz. E, On the logarithmic summability of sequences in intuitionistic fuzzy normed spaces,

    3(2), 101-108 (2020).

    [19] Zadeh .L .A, Fuzzy sets, Inf, control, 8, 338-353 (1965).

    Cite This Article As :
    Jeyaraman, M.. , Jenifer, P.. , Praveena, U.. New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces. Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, 2022, pp. 29-39. DOI: https://doi.org/10.54216/IJNS.190303
    Jeyaraman, M. Jenifer, P. Praveena, U. (2022). New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces. Journal of International Journal of Neutrosophic Science, 19( 3), 29-39. DOI: https://doi.org/10.54216/IJNS.190303
    Jeyaraman, M.. Jenifer, P.. Praveena, U.. New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces. Journal of International Journal of Neutrosophic Science 19, no. 3 (2022): 29-39. DOI: https://doi.org/10.54216/IJNS.190303
    Jeyaraman, M. , Jenifer, P. , Praveena, U. (2022) . New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces. Journal of International Journal of Neutrosophic Science , 19( 3) , 29-39 . DOI: https://doi.org/10.54216/IJNS.190303
    Jeyaraman M. , Jenifer P. , Praveena U. [2022]. New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces. Journal of International Journal of Neutrosophic Science. 19( 3): 29-39. DOI: https://doi.org/10.54216/IJNS.190303
    Jeyaraman, M. Jenifer, P. Praveena, U. "New Approach in Logarithmic Summability of Sequences in Neutrosophic Normed Spaces," Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 29-39, 2022. DOI: https://doi.org/10.54216/IJNS.190303