Hahn-banach Theorem for Functionals on Hypervector Spaces
-
2358
Downloads
-
4215
Views
Authors
Ali Taghavi
- Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran
Roja Hosseinzadeh
- Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran
Abstract
In this paper we prove Hahn-Banach Theorem for functionals on hypervector spaces. In this regard, we introduce a new category of hypervector spaces and prove some results for them.
Share and Cite
ISRP Style
Ali Taghavi, Roja Hosseinzadeh, Hahn-banach Theorem for Functionals on Hypervector Spaces, Journal of Mathematics and Computer Science, 2 (2011), no. 4, 682--690
AMA Style
Taghavi Ali, Hosseinzadeh Roja, Hahn-banach Theorem for Functionals on Hypervector Spaces. J Math Comput SCI-JM. (2011); 2(4):682--690
Chicago/Turabian Style
Taghavi, Ali, Hosseinzadeh, Roja. "Hahn-banach Theorem for Functionals on Hypervector Spaces." Journal of Mathematics and Computer Science, 2, no. 4 (2011): 682--690
Keywords
- hypervector space
- normed hypervector space
- functional.
MSC
References
-
[1]
R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2 (2005), 37--47
-
[2]
P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bulletin of Mathematics, 27 (2003), 221--229
-
[3]
P. Corsini, Prolegomena of hypergroup theory, Aviani editore, Italy (1993)
-
[4]
P. Corsini, V. Leoreanu, Applications of Hyperstructure theory, Kluwer Academic Publishers, Dordrecht (2003)
-
[5]
V. Leoreanu, Direct limits and inverse limits of SHR semigroups, Southeast Asian Bulletin of Mathematics, 25 (2001), 421--426
-
[6]
V. Leoreanu Fotea, L. Leoreanu, About a sequence of hyperstructures associated with a rough set, Southeast Asian Bulletin of Mathematics, Vol. 34, 113--119 (2010)
-
[7]
F. Marty, Sur une generalization de la notion de group, 8𝑡h Congress of the Scandinavian Mathematics (Stockholm), 1934 (1934), 45--49
-
[8]
S. Pianskool, W. Hemakul, S. Chaopraknoi, On Homomorphisms of Some Multiplicative Hyperrings, Southeast Asian Bulletin of Mathematics, 32 (2008), 951--958
-
[9]
A. Taghavi, R. Hosseinzadeh, A note on dimension of weak hypervector spaces, Italian J. Pure Appl. Math., 33 (2014), 7--14
-
[10]
A. Taghavi, R. Hosseinzadeh, Operators on normed hypervector spaces, Southeast Asian Bulletin of Mathematics, 35 (2011), 367--372
-
[11]
A. Taghavi, R. Parvinianzadeh, Hyperalgebras and Quotient Hyperalgebras, Italian J. Pure Appl. Math., 26 (2009), 17--24
-
[12]
M. Scafati-Tallini, Characterization of remarkable Hypervector space, Proc. 8th congress on Algebraic Hyperstructures and Aplications (Samotraki, Greece), 2002 (2002), 231--237
-
[13]
M. Scafati-Tallini, Weak Hypervector space and norms in such spaces, Algebraic Hyperstructures and Applications, 1994 (1994), 199--206
-
[14]
T. Vougiouklis, The fundamental relation in hyperrings, In: The general hyperfield: Algebraic hyperstructures and applications, 1991 (1991), 203--211
-
[15]
T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, Palm Harber (1994)