  The main goal of this paper is to characterize arbitrary nonlinear
(non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between
Banach spaces that satisfy a quite natural Pietsch Domination-type theorem
around a given point $(a_{1},...,a_{n})\in$ $X_{1}\times...\times X_{n}$. As a
consequence of our approach a notion of weighted summability arises naturally,
which may be an interesting topic for further investigation.
