Lie ternary $(\sigma,\tau,\xi)$--derivations on Banach ternary algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 4، دوره 9، شماره 1، آذر 2018، صفحه 41-53 اصل مقاله (403.18 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.3081 | ||
| نویسنده | ||
| Razieh Farokhzad Rostami* | ||
| Department of Mathematics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, Gonbad Kavous, Iran | ||
| چکیده | ||
| Let $A$ be a Banach ternary algebra over a scalar field $\Bbb R$ or $\Bbb C$ and $X$ be a ternary Banach $A$--module. Let $\sigma,\tau$ and $\xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)\to (X,[~]_X)$ is called a Lie ternary $(\sigma,\tau,\xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(\sigma,\tau,\xi)}-[[D(c)ba]_X]_{(\sigma,\tau,\xi)}$$ for all $a,b,c\in A$, where $[abc]_{(\sigma,\tau,\xi)}=a\tau(b)\xi(c)-\sigma(c)\tau(b)a$ and $[a,b,c]=[abc]_{A}-[cba]_{A}$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of Lie ternary $(\sigma,\tau,\xi)$--derivations on Banach ternary algebras and $C^*$--Lie ternary $(\sigma,\tau,\xi)$--derivations on $C^*$--ternary algebras for the following Euler--Lagrange type additive mapping: $$\sum_{i=1}^{n}f\textbf{(}\sum_{j=1}^{n}q(x_i-x_j)\textbf{)} +nf(\sum_{i=1}^{n}qx_i)=nq\sum_{i=1}^{n}f(x_i).$$ | ||
| کلیدواژهها | ||
| Banach ternary algebra؛ Lie ternary $(\sigma؛ \tau؛ \xi)$-derivation؛ Hyers-Ulam-Rassias stability | ||
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