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Hyperstability of a Cauchy functional equation. (English) Zbl 1413.39052

Summary: The aim of this paper is to offer hyperstability results for the Cauchy functional equation \[ f\bigg(\sum_{i=1}^{n}x_{i}\bigg)=\sum_{i=1}^{n}f(x_{i}) \] in Banach spaces. Namely, we show that a function satisfying the equation approximately must be actually a solution to it.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B62 Functional inequalities, including subadditivity, convexity, etc.
47H14 Perturbations of nonlinear operators
47H10 Fixed-point theorems
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