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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 \(f: G \to X\) 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 \(x, y \in G\). In this paper, the authors study the Hyers-Ulam-Rassias stability of the above functional equation in non-Archimedean 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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