Abstract.
A new stability concept is introduced which generalizes the notion of the Hyers–Ulam stability. The Cauchy functional equation is shown to be stable in this more general sense. The proof of this result is based on a new sandwich theorem proved also in this paper. As an application, quasiadditive functions in the sense of Józef Tabor are considered and stability and characterization theorems for them are obtained.
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Received: October, 1997; revised version: February 20, 1998
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Páles, Z. Generalized stability of the Cauchy functional equation. Aequ. math. 56, 222–232 (1998). https://doi.org/10.1007/s000100050058
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DOI: https://doi.org/10.1007/s000100050058