We investigate the generalized Hyers-Ulam-Rassias stability of the system of functional equations: f ( x y ) = f ( x ) f ( y ) , f ( 2 x + y ) + f ( 2 x − y ) = 2 f ( x + y ) + 2 f ( x − y ) + 12 f ( x ) , on Banach algebras. Indeed we establish the superstability of this system by suitable control functions.