Abstract
We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation that is close to a given approximate solution.
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Brzdęk, J., Leśniak, Z. & Malejki, R. On the generalized Fréchet functional equation with constant coefficients and its stability. Aequat. Math. 92, 355–373 (2018). https://doi.org/10.1007/s00010-017-0536-1
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DOI: https://doi.org/10.1007/s00010-017-0536-1