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Stability of functional equations in non-Archimedean spaces. (English) Zbl 1257.39019
Summary: We prove the generalized Hyers-Ulam stability of the Cauchy functional equation \(f(x+y) = f(x)+f(y)\) and the quadratic functional equation \(f(x+ y) f(x - y) = 2f(x) + 2f(y)\) in non-Archimedean normed spaces.

MSC:
39B22 Functional equations for real functions
39B82 Stability, separation, extension, and related topics for functional equations
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