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We give an answer to a problem formulated by Th. M. Rassias in 1991 concerning stability of the Cauchy equation; we also disprove a conjecture of Th. M. Rassias and J. Tabor. In particular, we present a new method for proving stability results for functional equations.

Note on stability of the Cauchy equation – an answer to a problem of Th. M. Rassias