Approximate multi-additive mappings in 2-Banach spaces

Document Type : Research Paper


AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland


A mapping $f:V^n \longrightarrow W$, where $V$ is a commutative
semigroup, $W$ 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].


Main Subjects