论文标题
通过Dunford-Pettis $ p $ - 会议运营商进行分解定理
Factorization Theorem through a Dunford-Pettis $p$-convergent operator
论文作者
论文摘要
在本文中，我们介绍了$ p $ - $（dpl）$集的概念。派生$ f^{\ prime} $将$ u $结合的集合用于$ p $ - $ - $（dpl）$ sets，并且仅在发生时才发生$ f = g \ circ s，$ s $是$ s $是dunford-pettis $ p $ p $ p $ contergent的$ x $ x $与合适的banach space $ z $ z $ z $ z $ z $ z $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ 特性。
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.
