Stability of multi-additive mappings in non-Archimedean normed spaces

A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n⩾1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers–Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.