Fixed Point Properties and Q -Nonexpansive Retractions in Locally Convex Spaces
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Publication Details
Author list: Dhompongsa S., Kumam P., Soori E.
Publisher: Birkhauser Verlag AG
Publication year: 2018
Volume number: 73
Issue number: 2
ISSN: 1422-6383
eISSN: 1422-6383
Languages: English-Great Britain (EN-GB)
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Abstract
Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space E has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck’s problem (Pacific J Math 53:59–71, 1974) for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups. © 2018, Springer International Publishing AG, part of Springer Nature.
Keywords
Q-nonexpansive mapping, retraction, right amenable semigroup, seminorm, Weak fixed point property
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