STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS

N. Eghbalı

doi:10.1501/Commua1_0000000727

STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS

Year 2015, Volume: 64 Issue: 1, 61 - 73, 01.02.2015

N. Eghbalı

https://doi.org/10.1501/Commua1_0000000727

Abstract

In this paper we introduce the concept of fuzzy Banach *-algebra.Then we study the stability and super stability of approximately *-homomorphismsin the fuzzy sense

Keywords

Fuzzy normed space, approximately *-homomorphism, stability

References

Z. Gajda, On stability of additive mappings, Intermat. J. Math. Sci., 14 (1991), 431–434.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431–436.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. (1941), 222–224.
B. E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc. 2 37 (1988), 294–316.
R. V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266.
R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, Vol. I: Elementary theory, Pure and Applied Mathematics, Vol. 100, Academic Press, New York, (1983).
A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143–
A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems, 159 (6) (2008), 720–729 .
C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. (2002), 711–720.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300.
Th. M. Rassias and P. Šemrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 173 (1993), 325–338.
S. M. Ulam, Problems in modern mathematics, Chap. VI, Science eds., Wiley, New York, L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338–353.
Address : Department of Mathematics, Facualty of Mathematical Sciences, University of Mo- haghegh Ardabili, 56199-11367, Ardabil, Iran.
E-mail : nasrineghbali@gmail.com,eghbali@uma.ac.ir Ba¸ slık: Bulanık yakla¸sık *-homomor…zmin kararlılı¼gı ve süper kararlılı¼gı Anahtar Kelimeler: Bulanık normlu uzay, yakla¸sık *-homomor…zm, kararlılık

Year 2015, Volume: 64 Issue: 1, 61 - 73, 01.02.2015

N. Eghbalı

https://doi.org/10.1501/Commua1_0000000727

Abstract

References

Z. Gajda, On stability of additive mappings, Intermat. J. Math. Sci., 14 (1991), 431–434.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431–436.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. (1941), 222–224.
B. E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc. 2 37 (1988), 294–316.
R. V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266.
R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, Vol. I: Elementary theory, Pure and Applied Mathematics, Vol. 100, Academic Press, New York, (1983).
A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143–
A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems, 159 (6) (2008), 720–729 .
C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. (2002), 711–720.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300.
Th. M. Rassias and P. Šemrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 173 (1993), 325–338.
S. M. Ulam, Problems in modern mathematics, Chap. VI, Science eds., Wiley, New York, L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338–353.
Address : Department of Mathematics, Facualty of Mathematical Sciences, University of Mo- haghegh Ardabili, 56199-11367, Ardabil, Iran.
E-mail : nasrineghbali@gmail.com,eghbali@uma.ac.ir Ba¸ slık: Bulanık yakla¸sık *-homomor…zmin kararlılı¼gı ve süper kararlılı¼gı Anahtar Kelimeler: Bulanık normlu uzay, yakla¸sık *-homomor…zm, kararlılık

There are 14 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	N. Eghbalı This is me
Publication Date	February 1, 2015
Published in Issue	Year 2015 Volume: 64 Issue: 1

Cite

APA	Eghbalı, N. (2015). STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(1), 61-73. https://doi.org/10.1501/Commua1_0000000727
AMA	Eghbalı N. STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2015;64(1):61-73. doi:10.1501/Commua1_0000000727
Chicago	Eghbalı, N. “STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64, no. 1 (February 2015): 61-73. https://doi.org/10.1501/Commua1_0000000727.
EndNote	Eghbalı N (February 1, 2015) STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64 1 61–73.
IEEE	N. Eghbalı, “STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY -HOMOMORPHISMS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.*, vol. 64, no. 1, pp. 61–73, 2015, doi: 10.1501/Commua1_0000000727.
ISNAD	Eghbalı, N. “STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY -HOMOMORPHISMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics* 64/1 (February 2015), 61-73. https://doi.org/10.1501/Commua1_0000000727.
JAMA	Eghbalı N. STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY -HOMOMORPHISMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.* 2015;64:61–73.
MLA	Eghbalı, N. “STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 64, no. 1, 2015, pp. 61-73, doi:10.1501/Commua1_0000000727.
Vancouver	Eghbalı N. STABILITY AND SUPER STABILITY OF FUZZY APPROXIMATELY *-HOMOMORPHISMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64(1):61-73.