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Stability of two types of cubic functional equations in non-archimedean spaces. (English) Zbl 1254.39015
Summary: We prove the generalized stability of the cubic type functional equation
\[ f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x) \] and another functional equation \[ f(ax+y)+f(x+ay)=(a+1)(a-1)2[f(x)+f(y)]+a(a+1)f(x+y), \]
where \(a\) is an integer with \(a\neq 0,\pm1\) in the framework of non-archimedean normed spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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