Nonexpansive Mappings in Locally Convex Spaces
Troy L. Hicks, John D. Kubicek · Canadian Mathematical Bulletin · 1977
Recently Bruck initiated the study of the structure of the fixed-point set of a nonexpansive selfmap T of a Banach space, where T satisfies a conditional fixed point property. We generalize many of his results to a Hausdorff locally convex space X. Also, we generalize a result of Holmes and Narayanaswami and use it, along with a procedure of Kiang, to obtain a fixed point theorem for families of asymptotically nonexpansive mappings in X.