In the present paper a solution of the generalized quadratic functional
f(kx + y) + f(kx + (y)) = 2k2f(x) + 2f(y), x, y 2 E
is given where is an involution of the normed space E and k is a fixed positive
integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the functional
equation. The Hyers-Ulam stability on unbounded domains is also studied.
Applications of the results for the asymptotic behavior of the generalized quadratic
functional equation are provided.