Some applications of p-(DPL) sets

In this paper, we introduce a new class of subsets of class bounded linear operators between Banach spaces which is called p-(DPL) sets. Then, the relationship between these sets with equicompact sets is investigated. Moreover, we define p-version of Right sequentially continuous differentiable mappings and get some characterizations of these mappings. Finally, we prove that a mapping f : X ? Y between real Banach spaces is Fr?chet differentiable and f? takes bounded sets into p-(DPL) sets if and only if f may be written in the form f = 1?S where the intermediate space is normed, S is a Dunford-Pettis p-convergent operator, and g is a G?teaux differentiable mapping with some additional properties.