  In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a
factorization result for differentiable mappings through Dunford-Pettis
$p$-convergent operators is investigated.\ Namely, if $ X ,Y $ are real Banach
spaces and $U$ is an open convex subset of $X,$ then we obtain that, given a
differentiable mapping $f: U\rightarrow Y$ its derivative $f^{\prime}$ takes
$U$-bounded sets into $p$-$(DPL)$ sets if and only if it happens $f=g\circ S,$
where $S$ is a Dunford-Pettis $p$-convergent operator from $X$ into a suitable
Banach space $Z$ and $g:S(U)\rightarrow Y$ is a G\^ateaux differentiable
mapping with some additional properties.

Functional Analysis