The first norm characterization of inner product spaces was given by Fréchet in 1935. In 1936, Jordan and von Neumann proved that a normed space X is an inner product space if and only if, the parallelogram law holds in X. Since then, many other characterizations have been proved. Let G be an abelian group, and let X be a nonarchimedean space. We study Hyers-Ulam stability for the Fréchet functional equation f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) where f is a map f: G → X. This is a joint work with Gastão Bettencourt.

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nonarchimedean space,Hyers-Ulam stability

• Mathematics - Natural Sciences