We investigate the stability problem for the following functional inequality ∥ α f ( ( x + y ) / 2 α ) + β f ( ( y + z ) / 2 β ) + γ f ( ( z + x ) / 2 γ ) ∥ ≤ ∥ f ( x + y + z ) ∥ on restricted domains of Banach modules over a C ∗ -algebra. As an application we study the asymptotic behavior of a generalized additive mapping.