Cubic $ \Gamma-n$ normed linear spaces
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DOI:
https://doi.org/10.26637/MJM0603/0028Abstract
This paper is aimed to propose the notion of cubic $\Gamma-n$-normed linear spaces based on the theory of cubic $n$-normed linear space, fuzzy $n$-normed linear space, interval valued fuzzy $n$-normed linear space and cubic sets. The concept of convergence and Cauchy sequences in cubic $\Gamma-n$-normed linear space are introduced and we provide some results on it. Also, this paper introduces the notion of completeness in cubic $\Gamma-n$-normed linear space.
Keywords:
Cubic Γ-n -normed linear space, cubic sets, cubic n -normed linear space, interval valued fuzzy n -normed linear spaceMathematics Subject Classification:
Mathematics- Pages: 643-647
- Date Published: 01-07-2018
- Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)
W.Barnes, On the $Gamma$-rings of Nobusawa, Pacific Journal of Mathematics, 18 (1966), 411-422.
S Gahler, Lineare 2-normietre raume,Math. Nachr, 28(1965), 1-43.
H. Gunawan and Mashadi, On $n$-normed spaces, Int. $J$. Math. Math. Sci., 27(10)(2001), 631-639.
YB Jun, CS Kim, and MS Kang, Cubic subalgebras and ideals of bck/bci-algebras, Far East Journal of Mathematical Sciences 44(2010), 239-250.
S Kalaiselvan and S Sivaramakrishnan. S. vijayabalaji, $n$-Normed left $Gamma$-linear space, International Journal of Applied Engineering Research, 10(72)(2015), 64-76.
A. K. Katsaras , Fuzzy topological vector spaces, Fuzzy sets and systems, 12 (1984), 143-154.
A. K. Katsaras and Dar B Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal of Mathematical Analysis and Applications, 58(1977), 135-146.
A. Malcheski, Strong convex n-normed spaces, Mat. Bilten, 21(1997), 81-102.
A. Misiak, n-inner product spaces, Math. Nachr, 140(1989), 299-319.
AL Narayanan and S Vijayabalaji, Fuzzy n-normed linear space, International Journal of Mathematics and Mathematical Sciences, 24(2005),3963-3977.
Nobuo Nobusawa, On a generalization of the ring theory, Osaka Journal of Mathematics, 1(1964), 81-89.
Md. Sabur Uddin and Payer Ahmed, Gamma vector spaces and their generalization, International Archive of Applied Sciences and Technology, 2(2011), 77-83.
S Vijayabalaji, S Anita Shanthi and N Thillaigovindan, Interval valued fuzzy n-normed linear space, Journal of Fundamental Sciences, 4(2008), 287-297.
S Vijayabalaji, N Thillaigovindan and Young-Bae Jun, Intuitionistic fuzzy n-normed linear space, Bulletin of the Korean Mathematical Society, 44(2007), 291-308.
S Vijayabalaji, Cubic n- Normed Linear Space, Lambert Academic Publishers, 2017.
S Vijayabalaji and S Sivaramakrishnan, A cubic set theoretical approach to linear space, Abstract and Applied Analysis, Hindawi, 2015.
L A Zadeh, Information and control, Fuzzy sets, 8(1965), $338-353$.
L A Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information sciences, $8(3)(1975), 199-249$.
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