APPROXIMATE MULTI-ADDITIVE MAPPINGS IN 2-BANACH SPACES

Abstract. A mapping f : V n _ W, where V is a commutative semi- group, W is a linear space and n is a positive integer, is called multi- additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011) 193{202].