  Let $X,Y,Z$ and $W$ be normed spaces and $f:X\times Y\times Z\longrightarrow
W $ be a bounded tri-linear mapping. In this Article, we define the topological
centers for bounded tri-linear mapping and we invistagate thier properties. We
study the relationships between weakly compactenss of bounded linear mappings
and regularity of bounded tri-linear mappings. For both bounded tri-linear
mappings $f$ and $g$, let $f$ factors through $g$, we present necessary and
suficient condition such that the extensions of $f$ factors through extensions
of $g$. Also we establish relations between regularity and factorization
property of bounded tri-linear mappings.
