TY - JOUR AU - JAVADIAN, A. AU - ESHAGHI GORDJI , M. AU - BAVAND SAVADKOUHI, M. PY - 2011 TI - APPROXIMATELY PARTIAL TERNARY QUADRATIC DERIVATIONS ON BANACH TERNARY ALGEBRAS JO - Journal of Nonlinear Sciences and Applications SP - 60-69 VL - 4 IS - 1 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.004.01.06 DO - 10.22436/jnsa.004.01.06 ID - JAVADIAN2011 ER -