p-(DPL)集的一些应用

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2305367a

M. Alikhani

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引用次数: 0

摘要

本文引入了Banach空间间一类有界线性算子的一个新的子集，称为p-(DPL)集。然后，研究了这些集合与等紧集合之间的关系。此外，我们定义了右序列连续可微映射的p型，并得到了这些映射的一些刻画。最后，我们证明了映射f: X ?实巴拿赫空间之间的Y等于Fr?可微的和f?取有界集合为p-(DPL)集合当且仅当f可以写成f = 1?S，其中中间空间是赋范的，S是Dunford-Pettis p收敛算子，g是g ?具有一些附加性质的托可微映射。

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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.

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