Park (Permuting triderivations and permuting trihomomorphisms in Banach algebras, preprint) introduced the following tri-additive s-functional inequality 1 \(\displaystyle \begin{aligned} \begin{array}{rcl} {} & &\displaystyle \| f(x+y, z-w, a+b) + f(x-y, z+w, a-b) \\ & &\displaystyle \qquad -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\| \\ & &\displaystyle \quad \le \left\| s \left(2f\left(\frac{x+y}{2}, z-w, a+b \right) + 2f\left(\frac{x-y}{2}, z+w, a-b\right) \right. \right. \\ & &\displaystyle \qquad \left. \left. -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\right)\right\| , \end{array} \end{aligned} \) where s is a fixed nonzero complex number with \(|s |< 1\) . Using the fixed point method, we prove the Hyers-Ulam stability and hyperstability of permuting triderivations and permuting trihomomorphisms in Banach algebras and unital \(C^*\) -algebras, associated with the tri-additive s-functional inequality (1).