On the Stability of Ternary AQ-Hom-Ders: Bridging Generalized AQ-Functional Equations
Abstract
This paper investigates the relationship between ternary $AQ$-hom-ders and the generalized $AQ$-functional equation (generalized $AQ$-$\mathbb{FE}$) within the framework of ternary Banach algebras (\textsf{TB}\textrm{A}). By considering the specific cases of $t=1$ and $t=2$, we establish a systematic connection between additive/quadratic mappings and their corresponding ternary $AQ$-hom-ders. The non-trivial nature of these mappings is demonstrated through concrete examples on matrix algebras, highlighting their relevance in non-commutative settings. Furthermore, we derive the solutions for the generalized $AQ$-$\mathbb{FE}$ and establish their Hyers–Ulam ({\rm HU}) stability. Finally, the {\rm HU} stability of these ternary $AQ$-hom-ders is rigorously investigated in \textsf{TB}\textrm{A} using the fixed point (\textsf{FP}) approach.
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