In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

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 $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

In this paper, modifying the construction of a C∗-ternary algebra from a given C∗-algebra, we define a proper CQ∗-ternary algebra from a given proper CQ∗-algebra. We investigate homomorphisms in proper CQ∗-ternary algebras and derivations on proper CQ∗-ternary algebras associated with the Cauchy functional inequality ‖f(x) + f(y) + f(z)‖ ≤ ‖f(x+ y + z)‖. We moreover prove the Hyers-Ulam stabili...

We consider two analogues of associativity for ternary algebras: total and partial associativity. Using the corresponding ternary associators, we define ternary analogues of alternative and assosymmetric algebras. On any ternary algebra the alternating sum [a, b, c] = abc − acb − bac + bca + cab − cba (the ternary analogue of the Lie bracket) defines a structure of an anticommutative ternary al...

and Applied Analysis 3 in the middle variable, and associative in the sense that x, y, z,w, v x, w, z, y , v x, y, z , w, v , and satisfies ‖ x, y, z ‖ ≤ ‖x‖ · ‖y‖ · ‖z‖ and ‖ x, x, x ‖ ‖x‖ see 45, 47 . Every left Hilbert C∗-module is a C∗-ternary algebra via the ternary product x, y, z : 〈x, y〉z. If a C∗-ternary algebra A, ·, ·, · has an identity, that is, an element e ∈ A such that x x, e, e ...