Factorization Theorem through a Dunford-Pettis $p$-convergent operator

Abstract

In this article, we introduce the notion of p-(DP L) 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 → Y its derivative f ′ takes U -bounded sets into p-(DP L) sets if and only if it happens f = g • S, where S is a Dunford-Pettis p-convergent operator from X into a suitable Banach space Z and g : S(U ) → Y is a Gâteaux differentiable mapping with some additional properties.