The notion of multi-normed space was introduced by H.G. Dales and M.E. Polyakov in \cite{D-P}. This concept is somewhat similar to operator sequence space and has some connections with operator spaces and Banach latices. In this talk, we investigate the stability (see \cite{RAS}) of the quadratic functional equation for mappings from linear spaces into multi-normed spaces (see \cite{D-M}). We then study an asymptotic behavior of the quadratic equation in the framework of multi-normed spaces.

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