Hyers–Ulam stability of ternary $(\sigma,\tau,\xi)$-derivations on $C^*$-ternary algebras

Let $q$ be a positive rational number and let $A$ be a $C^*$-ternary algebra. Let $\sigma$, $\tau$ and $\xi$ be linear maps on $A$. We prove the generalized Hyers–Ulam stability of Jordan ternary $(\sigma,\tau,\xi)$-derivations, ternary $(\sigma,\tau,\xi)$-derivations and Lie ternary $(\sigma,\tau,\xi)$-derivations in $A$ for the following Euler–Lagrange type additive mapping:
$$ \Biggl(\sum_{i=1}^nf\biggl(\sum_{j=1}^nq(x_i-x_j)\biggr)\biggr)+nf\biggl(\sum_{i=1}^nqx_i\biggr)=nq\sum_{i=1}^nf(x_i). $$