Geodesic
Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 3-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $q$ be a positive rational number and let $A$ be a $C^*$-ternary algebra. Let $\sigma$, $\tau$ and $\xi$ be linear maps on $A$. We prove the generalized Hyers–Ulam stability of Jordan ternary $(\sigma,\tau,\xi)$-derivations, ternary $(\sigma,\tau,\xi)$-derivations and Lie ternary $(\sigma,\tau,\xi)$-derivations in $A$ for the following Euler–Lagrange type additive mapping: $$ \Biggl(\sum_{i=1}^nf\biggl(\sum_{j=1}^nq(x_i-x_j)\biggr)\biggr)+nf\biggl(\sum_{i=1}^nqx_i\biggr)=nq\sum_{i=1}^nf(x_i). $$ 
@article{JMAG_2012_8_1_a0,
     author = {M. Eshaghi Gordji and R. Farrokhzad and S. A. R. Hosseinioun},
     title = {Hyers{\textendash}Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {3--20},
     year = {2012},
     volume = {8},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a0/}
}
TY  - JOUR
AU  - M. Eshaghi Gordji
AU  - R. Farrokhzad
AU  - S. A. R. Hosseinioun
TI  - Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2012
SP  - 3
EP  - 20
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a0/
LA  - en
ID  - JMAG_2012_8_1_a0
ER  - 
%0 Journal Article
%A M. Eshaghi Gordji
%A R. Farrokhzad
%A S. A. R. Hosseinioun
%T Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2012
%P 3-20
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a0/
%G en
%F JMAG_2012_8_1_a0
M. Eshaghi Gordji; R. Farrokhzad; S. A. R. Hosseinioun. Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a0/

[1] H. Zettl, “A Characterization of Ternary Rings of Operators”, Adv. Math., 48 (1983), 117–143 | DOI | MR | Zbl

[2] M. Amyari and M.S. Moslehian, “Approximately Homomorphisms of Ternary Semigroups”, Lett. Math. Phys., 77 (2006), 1–9 | DOI | MR | Zbl

[3] C. Park, “Generalized Hyers–Ulam Stability of $C^*$-Ternary Algebtra Homomorphisms”, Math. Anal., 16 (2009), 67–79 | MR | Zbl

[4] S.M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960 | MR | Zbl

[5] D.H. Hyers, “On the Stability of the Linear Functional Equation”, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222–224 | DOI | MR

[6] T. Aoki, “On the Stability of the Linear Transformation in Banach Spaces”, J. Math. Soc. Japan, 2 (1950), 64–66 | DOI | MR | Zbl

[7] Th.M. Rassias, “On the Stability of the Linear Mapping in Banach Spaces”, Proc. Amer. Math. Soc., 72 (1978), 297–300 | DOI | MR | Zbl

[8] Th.M. Rassias, “Problem 16”, 2, Report of the 27th International Symp. On Functional Equations, Aequationes Math., 39 (1990), 292–293; 309

[9] Z. Gajda, “On Stability of Additive Mappings”, Int. J. Math. Math. Sci., 14 (1991), 431–434 | DOI | MR | Zbl

[10] Th.M. Rassias and P. Šemrl, “On the Behaviour of Mappins which do not Satisfy Hyers–Ulam Stability”, Proc. Amer. Math. Soc., 114 (1992), 989–993 | DOI | MR | Zbl

[11] P. Gǎvrtua, “A Generalization of the Hyers–Ulam–Rassias Stability of Approximately Additive Mappings”, J. Math. Anal. Appl., 184 (1994), 431–436 | DOI | MR

[12] J.M. Rassias, “On Approximation of Approximately Linear Mapping by Linear Mappings”, Bull. Sci. Math., 108 (1984), 445–446 | MR | Zbl

[13] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hoong Kong, Singapore and London, 2002 | MR | Zbl

[14] M. Eshaghi Gordji, A. Ebadian, and S. Zolfaghari, “Stability of a Functional Equation Deriving from Cubic and Quartic Functions”, Abstr. Appl. Anal., 2008 (2008), 801904 | MR | Zbl

[15] M. Eshaghi Gordji and H. Khodaei, “Solution and Stability of Generalized Mixed Type Cubic, Quadratic and Additive Functional Equation in Quasi-Banach Spaces”, Nonlinear Analysis, 71 (2009), 5629–5643 | DOI | MR | Zbl

[16] D.H. Hyers, G. Isac, and Th.M. Rassias, Stability of Functional Equations in Several Variable, Birkhäuser, Basel, 1998 | MR | Zbl

[17] S.M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic press, Palm Harbor, Florida, 2001 | MR | Zbl

[18] C. Park, “Lie *-Homomorphisms between Lie $C^*$-Algebras”, J. Math. Anal. Appl., 293 (2004), 419–434 | DOI | MR | Zbl

[19] C. Park, “Homomorphisms between Lie $JC^*$-Algebras and Cauchy–Rassias Stability of Lie $JC^*$-Algebra Derivations”, J. Lie Theory, 15 (2005), 393–414 | MR | Zbl

[20] J.M. Rassias, “On the Stability of the Euler–Lagrange Functional Equation”, Chinese J. Math., 20 (1992), 185–190 | MR | Zbl

[21] J.M. Rassias, “Solution of the Ulam Stability Problem for Euler–Lagrange Quadratic Mappings”, J. Math. Anal. Appl., 220 (1998), 1613–639 | DOI | MR

[22] J.M. Rassias and M.J. Rassias, “On the Ulam Stability for Euler–Lagrange Type Quadratic Functional Equations”, Austral. J. Math. Anal. Appl., 2 (2005), 1–10 | MR | Zbl

[23] M. Bavand Savadkouhi, M. Eshaghi Gordji, J.M. Rassias, and N. Ghobadipour, “Approximate Ternary Jordan Derivations on Banach Ternary Algebras”, J. Math. Phys., 50:4 (2009), 042103, 19 pp. | DOI | MR

[24] C. Park, “Homomorphisms between Poisson $JC^*$-Algebras”, Bull. Braz. Math. Soc., 36 (2005), 79–97 | DOI | MR | Zbl

[25] C. Park, “Hyers–Ulam–Rassias Stability of a Generalized Euler–Lagrange Type Additive Mapping and Isomorphisms between $C^*$-Algebras”, Bull. Belgian Math. Soc.-Simon Stevin, 13 (2006), 619–631 | MR