2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222505In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y), \qquad\qquad. f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x), $$ on Banach algebras. Indeed we establish the superstability of above system by suitable control functions.11 pagesClassical Analysis and ODEsFunctional Analysis46H25text