In this paper, we prove the Hyers-Ulam stability problem for the following function inequalities parallel to Sigma(N)(i=1) f(x(i))parallel to <= parallel to K f(Sigma(N)(i=1) x(i)/K)parallel to parallel to Sigma(N)(i=1) f(x(i))parallel to <= parallel to K f(Sigma(m)(i=1) x(i)/K) + C f(Sigma(N)(i=m+1) x(i)/C)parallel to in beta-homogeneous F-spaces.