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Amenability and fixed point properties of semi-topological semigroups of non-expansive mappings in Banach spaces
In this thesis we are interested in fixed point properties of representations of semi-topological semigroups of non-expansive mappings on weak and weak* compact convex sets in Banach or dual spaces. More particularly, we study the following problems : Problem 1 : Let F be any commuting family of non-expansive mappings on a non-empty weakly compact convex subset of a Banach space such that for each f ∈ F there is an x whose f -orbit has a cluster point (in the norm topology). Does F possess adoi:10.7939/r35717w55 fatcat:4m4v6b5ngvfszf4pmoyx7soyhm