On summability of nonlinear mappings: a new approach

The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_1\times \mathrm{.}\mathrm{.}\mathrm{.}\times X_n\to Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_n)\in$ $X_1\times \mathrm{.}\mathrm{.}\mathrm{.}\times X_n$. As a consequence of our approach a notion of weighted summability arises naturally, which may be an interesting topic for further investigation.