Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in C*-Ternary Algebras

In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in (Formula presented.) -ternary algebras. The study of functional equations with a sufficient number of variables can be helpful in solving real-world problems such as artificial intelligence. In this paper, we build on previous research on functional equations with four variables to study functional equations with as many variables as desired. We introduce new bounds for the stability of mappings satisfying generalized bi-additive conditions and demonstrate the uniqueness of approximating bi-isomorphisms. The results contribute to the deeper understanding of ternary algebraic structures and related functional equations, relevant to both pure mathematics and quantum information science.