In this paper, we prove the Hyers-Ulam stability of C ∗ -ternary 3-derivations and of C ∗ -ternary 3-homomorphisms for the functional equation f ( x 1 + x 2 , y 1 + y 2 , z 1 + z 2 ) = ∑ 1 ≤ i , j , k ≤ 2 f ( x i , y j , z k ) in C ∗ -ternary algebras. MSC:17A40, 39B52, 46Lxx, 46K70, 46L05, 46B99.

In this article, we solve the system of additive functional equations: 2 f ( x + y ) − g ( x ) = g ( y ) , g ( x + y ) − 2 f ( y − x ) = 4 f ( x ) and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f -hom-ders in Banach algebras.

Using the Brzdek fixed point theorem, we establish the Hyers?Ulam stability problem of Drygas functional equations \begin{equation} \delta(x+y-z)+\delta(x-y)+\delta(-y-z)+\delta(y)=\delta(x-y-z)+\delta(y-z)+\delta(x+y)+\delta(-y)\nonumber \end{equation} for all $x,y,z\in A$.