Geodesic
Nonexpansive Mappings in Locally Convex Spaces
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 455-461

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DOI

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. 
Hicks, Troy L.; Kubicek, John D. Nonexpansive Mappings in Locally Convex Spaces. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 455-461. doi: 10.4153/CMB-1977-067-9
@article{10_4153_CMB_1977_067_9,
     author = {Hicks, Troy L. and Kubicek, John D.},
     title = {Nonexpansive {Mappings} in {Locally} {Convex} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {455--461},
     year = {1977},
     volume = {20},
     number = {4},
     doi = {10.4153/CMB-1977-067-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-067-9/}
}
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