Separable Determination of the Fixed Point Property of Convex Sets in Banach Spaces
Year: 2016
Author: Qingxia Li, Lili Su, Qian Wei
Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 33–41
Abstract
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 c0(Γ) (for any set Γ) is again lying in c0. 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 c0(Γ) has a fixed point.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n1.16.04
Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 33–41
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Non-expansive mapping weakly compact convex set fixed point Banach space.
Author Details
Qingxia Li Email
Lili Su Email
Qian Wei Email