APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS


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


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