Volume 19 , Issue 3 , PP: 29-39, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
M. Jeyaraman 1 * , P. Jenifer 2 , U. Praveena 3
Doi: https://doi.org/10.54216/IJNS.190303
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.
Neutrosophic Normed Spaces , Logarithm Summability , Slow Oscillation , Taubarian Theorem.
[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).