Common fixed points for semigroups of mappings

Lau, Anthony T.; Wong, Chi Song

doi:10.1090/S0002-9939-1973-0322837-3

Common fixed points for semigroups of mappings
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by Anthony T. Lau and Chi Song Wong PDF

Proc. Amer. Math. Soc. 41 (1973), 223-228 Request permission

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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Fixed point theorems on compact Hausdorff spaces

Fixed points of generalised nonexpansive mappings on an into