Abstract
We present some simple observations on hyperstability for the Cauchy equation on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense), must be actually solutions to it. In this way we demonstrate in particular that hyperstability is not a very exceptional phenomenon as it has been considered so far. We also provide some simple examples of applications of those results.
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Brzdȩk , J. Remarks on hyperstability of the Cauchy functional equation. Aequat. Math. 86, 255–267 (2013). https://doi.org/10.1007/s00010-012-0168-4
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DOI: https://doi.org/10.1007/s00010-012-0168-4