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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2012, Volume 8, Number 1, Pages 3–20
(Mi jmag522)
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This article is cited in 2 scientific papers (total in 2 papers)
Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras
M. Eshaghi Gordjia, R. Farrokhzadb, S. A. R. Hosseiniounb a Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran;
Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Iran
b Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Abstract:
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:
$$
\Biggl(\sum_{i=1}^nf\biggl(\sum_{j=1}^nq(x_i-x_j)\biggr)\biggr)+nf\biggl(\sum_{i=1}^nqx_i\biggr)=nq\sum_{i=1}^nf(x_i).
$$
Key words and phrases:
$C^*$-ternary algebra, Hyers–Ulam stability, ternary Banach algebra, Euler–Lagrange type additive mapping.
Received: 08.10.2009
Citation:
M. Eshaghi Gordji, R. Farrokhzad, S. A. R. Hosseinioun, “Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras”, Zh. Mat. Fiz. Anal. Geom., 8:1 (2012), 3–20
Linking options:
https://www.mathnet.ru/eng/jmag522 https://www.mathnet.ru/eng/jmag/v8/i1/p3
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Abstract page: | 252 | Full-text PDF : | 60 | References: | 30 |
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