This is an announcement for the paper “Factorization Theorem through a Dunford-Pettis $p$-convergent operator” by Morteza Alikhanihttps://arxiv.org/search/math?searchtype=author&query=Alikhani%2C+M.

Abstract: 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 Gâteaux differentiable mapping with some additional properties.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.01163