The fixed-point property in Banach spaces containing a copy of c0

Abstract

We prove that every Banach space containing an isomorphic copy of c0 fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy of c0 is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.