Browse > Article
http://dx.doi.org/10.14403/jcms.2010.23.3.563

ON THE STABILITY OF GENERALIZED DERIVATION IN FUZZY BANACH ALGEBRA  

Chang, Ick-Soon (Department of Mathematics Mokwon University)
Kim, Min-Young (Department of Mathematics Chungnam University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.3, 2010 , pp. 563-570 More about this Journal
Abstract
In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.
Keywords
generalized derivation; fuzzy stability;
Citations & Related Records
연도 인용수 순위
  • Reference
1 I. Sadeqi and A. Amiripour, Fuzzy Banach algebra, First joint congress on fuzzy and intelligent systems, Ferdorwsi university of mashhad, Iran, 29-31 Aug 2007.
2 P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integr. Equat. Oper. Theory 18 (1994), 118-122.   DOI
3 S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York (1968), p.63.
4 J.-Z. Xiao and X.-H. Zhu, Fuzzy normed linear spaces of operators and its completeness, Fuzzy sets and systems 133 (2003), 389-399.   DOI   ScienceOn
5 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc., Japan 2 (1950), 64-66.   DOI
6 R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), 589-597.   DOI   ScienceOn
7 R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), 167-173.
8 T. Bag and S. K. Samanta, Finite diemensional fuzzy normed linear spaces, J. Fuzzy Math 11 (2003), 687-705.
9 T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy sets and systems 151 (2005), 513-547.   DOI   ScienceOn
10 D. G . Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.   DOI
11 D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. (N.S.), 57 (1951), 223-237.   DOI
12 I.-S. Chang and Y.-S. Jung, Stability for the functional equation of cubic type, J. Math. Anal. Appl. 334 (2007), 85-96.   DOI   ScienceOn
13 S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), 429-436.
14 Felbin, Finite diemensional fuzzy normed linear spaces, Fuzzy sets and systems 48 (1992), 239-248.   DOI   ScienceOn
15 Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434.   DOI   ScienceOn
16 I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326-334.
17 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.   DOI   ScienceOn
18 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224.   DOI   ScienceOn
19 A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy sets and systems 12 (1984), 143-154.   DOI   ScienceOn
20 S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy sets and systems 63 (1994), 207-214.   DOI   ScienceOn
21 A. K. Mirmostafaee, M. Mirzavaziri and M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy sets and systems 159 (2008), 730-738.   DOI   ScienceOn
22 A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam- Rassias theorem, Fuzzy sets and systems 159 (2008), 720-729.   DOI   ScienceOn
23 A. K. Mirmostafaee and M. S. Moslehian, Fuzzy approximately cubic mappings, Inform. Sci. 178 (2008), 3791-3798.   DOI   ScienceOn
24 A. K. Mirmostafaee and M.S. Moslehian, Fuzzy almost quadratic functions, Results Math. 52 (2008), 161-171.   DOI   ScienceOn
25 T. Miura, G. Hirasawa and S.-E. Takahasi, A perturbation of ring derivations on Banach algebras, J. Math. Anal. Appl. 319 (2006), 522-530.   DOI   ScienceOn
26 Th. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI   ScienceOn