Weakly $p$-sequentially continuous differentiable mappings

In this paper, we introduce the notions uniformly p-convergent sets and weakly p-sequentially continuous differentiable mappings. Then we obtain a sufficient condition for those Banach spaces which either contain no copy of ${\mathrm{\ell }}_1$ or have the p-Schur property. Finally, we obtain a characterization for the weakly p-sequentially continuous differentiable mappings.