Stability of multi-additive mappings in non-Archimedean normed spaces.(English)Zbl 1204.39027

Let $$V$$ be a commutative semigroup, $$W$$ a non-Archimedean space and $$n \geq 1$$ an integer. A function $$f : V^n \to W$$ is said to be multi-additive if it is additive in each variable. In this paper, the author proves some results concerning the generalized Hyers-Ulam stability of the multi-additive functions in non-Archimedean spaces, using the direct method.

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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