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Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces. (English) Zbl 1204.39028

Let G be an additive group and X a complete non-Archimedean normed space. Let the function f:GX satisfy the functional equation

f(x+2y)+f(x-2y)=4(f(x+y)+f(x-y))-24f(y)-6f(x)+3f(2y)

for all x,yG. In this paper, the authors study the Hyers-Ulam-Rassias stability of the above functional equation in non-Archimedean spaces.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
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