Assume $H_i : R_+ imes R_+ o R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q leq 1)$ hold for $t, u, v geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $Vert f(x+y) - f(x)f(y) Vert leq H_i (Vert x Vert, Vert y Vert)$ shall be investigated.