APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS

JAVADIAN, A.¹ ; ESHAGHI GORDJI , M.² ; BAVAND SAVADKOUHI, M.²

¹ Department of Physics, Semnan University, P. O. Box 35195-363, Semnan, Iran
² Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 1, p. 60-69.

Résumé

Let $A_1,A_2,...,A_n$ be normed ternary algebras over the complex field $\mathbb{C}$ and let $B$ be a Banach ternary algebra over $\mathbb{C}$. A mapping $\delta_k$ from $A_1 \times ...\times A_n$ into $B$ is called a k-th partial ternary quadratic derivation if there exists a mapping $g_k : A_k \rightarrow B$ such that

$\delta_k(x_1,..., [a_kb_kc_k],..., x_n) =[g_k(a_k)g_k(b_k)\delta_k(x_1 ,..., c_k,..., xn)] + [g_k(a_k)\delta_k(x_1,..., b_k,..., x_n)g_k(c_k)] + [\delta_k(x_1,...,a_k,..., x_n)g_k(b_k)g_k(c_k)]$

and

$\delta_k(x_1,..., a_k + b_k,..., x_n) + \delta_k(x_1,... a_k - b_k,..., x_n) = 2\delta_k(x_1,..., a_k,..., x_n) + 2\delta_k(x_1,...,b_k,..., x_n)$

for all $a_k, b_k, c_k \in A_k$ and all $x_i \in A_i (i \neq k)$. We prove the Hyers-Ulam- Rassias stability of the partial ternary quadratic derivations in Banach ternary algebras.

Détail

DOI : 10.22436/jnsa.004.01.06

Classification : 46K05, 39B82, 39B52, 47B47
Keywords: Hyers-Ulam-Rassias stability, Banach ternary algebra, Partial ternary quadratic derivation.

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