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We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functionalequations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations whilewe investigate the stability of functional equations

A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations