Hyers–Ulam–Rassias Stability of Generalized Quadratic Functional Equation on Non-Archimedean Normed Space over p-Adic Numbers

We investigate the Hyers–Ulam–Rassias stability of a generalized quadratic functional equation of the asymmetric four-function form F(x+y)+G(x−y)=L(x)+M(y), where F, G, L, and M are unknown mappings. This study is conducted within the framework of non-Archimedean normed spaces over the p-adic numbers. Our approach employs a separation technique, analyzing the even and odd parts of the functions to establish stability results. We show that all four functions are approximated by a combination of a quadratic function and two additive functions.