@Article{JMS-49-1,
author = {Qingxia, Li and Su, Lili and Wei, Qian},
title = {Separable Determination of the Fixed Point Property of Convex Sets in Banach Spaces},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {1},
pages = {33--41},
abstract = {<p style="text-align: justify;">In this paper, we first show that for every mapping $f$ from a metric space $Ω$ to itself which is continuous off a countable subset of $Ω,$ there exists a nonempty
closed separable subspace $S ⊂ Ω$ so that $f|_S$ is again a self mapping on $S.$ Therefore,
both the fixed point property and the weak fixed point property of a nonempty closed
convex set in a Banach space are separably determined. We then prove that every
separable subspace of $c_0(\Gamma)$ (for any set $\Gamma$) is again lying in $c_0.$ Making use of these
results, we finally presents a simple proof of the famous result: Every non-expansive
self-mapping defined on a nonempty weakly compact convex set of $c_0(\Gamma)$ has a fixed
point.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n1.16.04},
url = {https://global-sci.com/article/87787/separable-determination-of-the-fixed-point-property-of-convex-sets-in-banach-spaces}
}