A Generalized Bi-Quadratic–Drygas Functional System in Non-Archimedean Normed Spaces over p-Adic Numbers

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.