On subadditive functions and ψ-additive mappings

In 4], assuming among others subadditivity and submultiplicavity of a function ψ: 0, ∞)→0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive