Permuting triderivations and permuting trihomomorphisms in complex Banach algebras

In this paper, we introduce and solve new tri-additive s-functional inequalities. Moreover, we prove the Hyers-Ulam staility and hyperstability of permuting triderivations and permuting trihomomorphisms in Banach algebras and unital \(C^*\) $C^{\ast }$ -algebras, associated with the new tri-additive s-functional inequalities.