This work investigates the solution and the stability of a generalized system of bi-quadratic–Drygas functional equations in non-Archimedean normed spaces with unknown coefficients. The presence of asymmetric coefficients and reflection terms induces nontrivial coupling effects and symmetry-breaking phenomena, while simultaneously capturing additive, quadratic, and mixed additive–quadratic behaviors. An examination of the coefficients shows that the trivial solution is the only one satisfying the system of equations in asymmetric parameter configurations. For symmetric configurations, by exploiting the ultrametric structure of non-Archimedean norms and applying an iterative method combined with symmetry-based decomposition into even and odd parts, we establish the existence and uniqueness of an exact solution approximating a given mapping. Several known stability results for bi-Drygas functional equations are recovered with improvement as special cases.

We establish two definitions of the convolution of vector measures on locally compact groups by employing injective tensor integration. These two formulations are shown to be isomorphic. We further investigate fundamental properties of the convolution of vector measures, including a representation in terms of double integrals and its behavior under the Fourier transform. In particular, we demonstrate that the Fourier transform of the convolution admits a factorization analogous to the classical case, with an inherent asymmetry arising from the vector-valued setting.

This paper investigates the Hyers–Ulam stability of a class of generalized biquadratic functional equations involving four unknown mappings in non‐Archimedean normed spaces. We analyze a coupled system that simultaneously incorporates additive, quadratic, additive–quadratic, and quadratic–additive behaviors, thereby capturing both symmetric and asymmetric interactions among the variables. By exploiting the ultrametric structure inherent in non‐Archimedean normed spaces, we establish the existence and uniqueness of approximating solutions, together with stability bounds. Furthermore, a known stability result for biquadratic functional equations is recovered as a corollary of the main theorem.