Browse > Article
http://dx.doi.org/10.11568/kjm.2014.22.4.659

FUZZY ALGEBRA HOMOMORPHISMS AND FUZZY DERIVATIONS  

Lee, Jung Rye (Department of Mathematics Daejin University)
Publication Information
Korean Journal of Mathematics / v.22, no.4, 2014 , pp. 659-670 More about this Journal
Abstract
In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.
Keywords
fuzzy Banach algebra; fuzzy algebra homomorphism; fuzzy derivation; Hyers-Ulam stability; Cauchy-Jensen functional equation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.   DOI
2 T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), 687-705.
3 T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems 151 (2005), 513-547.   DOI   ScienceOn
4 L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003).
5 L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43-52.
6 L. Cadariu and V. Radu, Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory and Applications 2008, Art. ID 749392 (2008).
7 S.C. Cheng and J.M. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), 429-436.
8 Y. Cho, C. Park and R. Saadati, Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Letters 23 (2010), 1238-1242.   DOI   ScienceOn
9 P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76-86.   DOI   ScienceOn
10 S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64.   DOI   ScienceOn
11 S. Czerwik, The stability of the quadratic functional equation. in: Stability of mappings of Hyers-Ulam type, (ed. Th.M. Rassias and J.Tabor), Hadronic Press, Palm Harbor, Florida, 1994, 81-91.
12 P. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002.
13 J. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.   DOI
14 M. Eshaghi Gordji and M.B. Savadkouhi, Approximation of generalized homo-morphisms in quasi-Banach algebras, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 17 (2009), No. 2, 203-213.
15 M. Eshaghi Gordji, A characterization of $({\sigma},{\tau})$-derivations on von Neumann algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A-Appl. Math. Phys. 73 (2011), No. 1, 111-116.
16 M. Eshaghi Gordji, A. Bodaghi and C. Park, A fixed point approach to the stability of double Jordan centralizers and Jordan multipliers on Banach algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A-Appl. Math. Phys. 73 (2011), No. 2, 65-74.
17 M. Eshaghi Gordji, H. Khodaei and R. Khodabakhsh, General quartic-cubic-quadratic functional equation in non-Archimedean normed spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A-Appl. Math. Phys. 72 (2010), No. 3, 69-84.
18 C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems 48 (1992), 239-248.   DOI   ScienceOn
19 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
20 D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224.   DOI   ScienceOn
21 D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.
22 G. Isac and Th.M. Rassias, Stability of $\psi$-additive mappings: Appications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996), 219-228.   DOI   ScienceOn
23 S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press lnc., Palm Harbor, Florida, 2001.
24 D. Mihet and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572.   DOI   ScienceOn
25 A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984), 143-154.   DOI   ScienceOn
26 I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326-334.
27 S.V. Krishna and K.K.M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems 63 (1994), 207-217.   DOI   ScienceOn
28 M. Mirzavaziri and M.S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37 (2006), 361-376.   DOI   ScienceOn
29 A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems 159 (2008), 720-729.   DOI   ScienceOn
30 A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inform. Sci. 178 (2008), 3791-3798.   DOI   ScienceOn
31 C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Applications 2007, Art. ID 50175 (2007).
32 C. Park, Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach, Fixed Point Theory and Applications 2008, Art. ID 493751 (2008).
33 V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91-96.
34 Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI   ScienceOn
35 J.Z. Xiao and X.H. Zhu, Fuzzy normed spaces of operators and its completeness, Fuzzy Sets and Systems 133 (2003), 389-399.   DOI   ScienceOn
36 R. Saadati and C. Park, Non-Archimedean L-fuzzy normed spaces and stability of functional equations, Computers Math. Appl. 60 (2010), 2488-2496.   DOI   ScienceOn
37 F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129.   DOI   ScienceOn
38 S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
39 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