Document Zbl 1257.39019

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Moslehian, Mohammad Sal; Rassias, Themistocles M.

Stability of functional equations in non-Archimedean spaces. (English) Zbl 1257.39019

Appl. Anal. Discrete Math. 1, No. 2, 325-334 (2007).

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.

Cited in 12 Reviews

Cited in 84 Documents

MSC:

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

Keywords:

generalized Hyers-Ulam stability; Cauchy functional equation; quadratic functional equation; non-Archimedean space; \(p\)-adic field

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