On Functions with the Cauchy Difference Bounded by a Functional
K. Baron and Z. Kominek [2] have studied the functional inequality f(x+y) - f(x) - f(y) ≥ ϕ (x,y), x, y ∈ X, under the assumptions that X is a real linear space, ϕ is homogeneous with respect to the second variable and f satisfies certain regularity conditions. In particular, they have shown that ϕ is bilinear and symmetric and f has a representation of the form f(x) = ½ ϕ(x,x) + L(x) for x ∈ X, where L is a linear function. The purpose of the present...