FUZZY n-INNER PRODUCT SPACE

Title & Authors
FUZZY n-INNER PRODUCT SPACE
Vijayabalaji, Srinivasan; Thillaigovindan, Natesan;

Abstract
The purpose of this paper is to introduce the notion of fuzzy n-inner product space. Ascending family of quasi $\small{{\alpha}}$-n-norms corresponding to fuzzy quasi n-norm is introduced and we provide some results on it.
Keywords
n-inner product;fuzzy n-inner product;fuzzy quasi n-norm;quasi $\small{{\alpha}}$-no-norm;
Language
English
Cited by
References
1.
A. M. El-Abyad and H. M. El-Hamouly, Fuzzy inner product spaces, Fuzzy Sets and Systems 44 (1991), no. 2, 309-326

2.
T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), no. 3, 687-705

3.
S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), no. 5, 429-436

4.
Y. J. Cho, M. Matic, and J. Pecaric, Inequalities of Hlawka's type in n-inner product spaces, Commun. Korean Math. Soc. 17 (2002), no. 4, 583-592

5.
Y. J. Cho, P. C. S. Lin, S. S. Kim, and A. Misiak, Theory of 2-inner product spaces, Nova Science Publishers, Inc., Huntington, NY, 2001

6.
C. Diminnie, S. GAahler, and A. White, 2-inner product spaces, Demonstratio Math. 6 (1973), 525-536

7.
C. Diminnie, S. GAahler, and A. White, 2-inner product spaces. II, Demonstratio Math. 10 (1977), no. 1, 169-188

8.
C. Felbin, Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems 48 (1992), no. 2, 239-248

9.
C. Felbin, The completion of a fuzzy normed linear space, J. Math. Anal. Appl. 174 (1993), no. 2, 428-440

10.
C. Felbin, Finite dimensional fuzzy normed linear space. II, J. Anal. 7 (1999), 117-131

11.
S. GAahler, Lineare 2-normierte RAaume, Math. Nachr. 28 (1964), 1-43

12.
S. GAahler, Untersuchungen Auber verallgemeinerte m-metrische Raume, I, II, III, Math. Nachr. 40 (1969), 165-189

13.
H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (2001), no. 10, 631-639

14.
A. K. Katsaras, Fuzzy topological vector spaces. II, Fuzzy Sets and Systems 12 (1984), no. 2, 143-154

15.
S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math. 29 (1996), no. 4, 739-744

16.
J. K. Kohli and R. Kumar, On fuzzy inner product spaces and fuzzy co-inner product spaces, Fuzzy Sets and Systems 53 (1993), no. 2, 227-232

17.
J. K. Kohli and R. Kumar, Linear mappings, fuzzy linear spaces, fuzzy inner product spaces and fuzzy co-inner product spaces, Bull. Calcutta Math. Soc. 87 (1995), no. 3, 237-246

18.
S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems 63 (1994), no. 2, 207-217

19.
R. Mal.ceski, Strong n-convex n-normed spaces, Mat. Bilten No. 21 (1997), 81-102

20.
A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319

21.
A. Misiak, Orthogonality and orthonormality in n-inner product spaces, Math. Nachr. 143 (1989), 249-261

22.
Al. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int. J. Math. Math. Sci. 2005 (2005), no. 24, 3963-3977

23.
G. S. Rhie, B. M. Choi, and D. S. Kim, On the completeness of fuzzy normed linear spaces, Math. Japon. 45 (1997), no. 1, 33-37