Local stability of the additive functional equation and its applications.
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Jung, Soon-Mo, Kim, Byungbae (2003)
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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
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International Journal of Mathematics and Mathematical Sciences
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