APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS
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Authors
A. JAVADIAN
- Department of Physics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
M. ESHAGHI GORDJI
- Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
M. BAVAND SAVADKOUHI
- Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
Abstract
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.
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ISRP Style
A. JAVADIAN, M. ESHAGHI GORDJI, M. BAVAND SAVADKOUHI, APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 1, 60-69
AMA Style
JAVADIAN A., ESHAGHI GORDJI M., BAVAND SAVADKOUHI M., APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS. J. Nonlinear Sci. Appl. (2011); 4(1):60-69
Chicago/Turabian Style
JAVADIAN, A., ESHAGHI GORDJI , M., BAVAND SAVADKOUHI, M.. " APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS." Journal of Nonlinear Sciences and Applications, 4, no. 1 (2011): 60-69
Keywords
- Hyers-Ulam-Rassias stability
- Banach ternary algebra
- Partial ternary quadratic derivation.
MSC
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