In this paper, it is shown that if f satisfies the following functional inequality (0.1) $${parallel}sumlimits_{i,j=1}^3;f{(xi,yj)}{parallel}{leq}{parallel}f(x_1+x_2+x_3,;y_1+y_2+y_3){parallel}$$ then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) $${parallel}2sumlimits_{j=1}^3;f{(x_j,;z)}+2sumlimits_{j=1}^3;f{(x_j,;w)-f(sumlimits_{j=1}^3;xj,;z-w)}{parallel}{leq}f(sumlimits_{j=1}^3;xj,;z+w){parallel}$$ then f is an additive-quadratic mapping.