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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References:

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