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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Common fixed points for semigroups of mappings

Authors: Anthony T. Lau and Chi Song Wong
Journal: Proc. Amer. Math. Soc. 41 (1973), 223-228
MSC: Primary 54H15; Secondary 47H10
MathSciNet review: 0322837
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Abstract: Let $ X$ be a compact convex subset of a strictly convex Banach space. Let $ S$ be a Hausdorff topological semigroup which is either left amenable or left reversible. Then for any generalised nonexpansive (jointly) continuous action of $ S$ on $ X,X$ contains a common fixed point of $ S$.

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PII: S 0002-9939(1973)0322837-3
Keywords: Common fixed points, equicontinuous mapping, generalized nonexpansive mapping, left amenable topological semigroup, left reversible topological semigroup, strictly convex Banach space, strongly almost periodic function
Article copyright: © Copyright 1973 American Mathematical Society