Fixed point properties for nonexpansive representations of topological semigroups (Q860566)

The authors establish new results on the existence of fixed points for nonexpansive mappings in Hilbert spaces. They extend the well-known Goebel--Schöneberg theorem [\textit{K.\,Goebel} and \textit{R.\,Schöneberg}, Bull.\ Aust.\ Math.\ Soc.\ 17, 463--466 (1977; Zbl 0365.47031)] to nonexpansive continuous representations of an amenable semitopological semigroup on a subset of a Hilbert space.