Weakly $p$-sequentially continuous differentiable mappings

TL;DR

This paper introduces new concepts of weakly p-sequentially continuous differentiable mappings and uniformly p-convergent sets, providing conditions on Banach spaces and characterizations of these mappings.

Contribution

It defines new notions in the theory of differentiable mappings and characterizes their behavior in specific Banach space settings.

Findings

Characterization of weakly p-sequentially continuous differentiable mappings

Sufficient conditions for Banach spaces related to $ ext{ell}_1$ and p-Schur property

Introduction of uniformly p-convergent sets

Abstract

In this paper, we introduce the notions uniformly p-convergent sets and weakly p-sequentially continuous differentiable mappings. Then we obtain a sufficient condition for those Banach spaces which either contain no copy of $\ell_1$ or have the p-Schur property. Finally, we obtain a characterization for the weakly p-sequentially continuous differentiable mappings.