Fixed points of isometries on weakly compact convex sets
In this paper, we prove that every isometry from a nonempty weakly compact convex set K into itself fixes a point in the Chebyshev center of K, provided K satisfies the hereditary fixed point property for isometries. In particular, all isometrics from a nonempty bounded closed convex subset of a uniformly convex Banach space into itself have the Chebyshev center as a common fixed point. © 2003 Elsevier Science (USA). All rights reserved.
Journal of Mathematical Analysis and Applications
Lim, T., Lin, P., Petalas, C., & Vidalis, T. (2003). Fixed points of isometries on weakly compact convex sets. Journal of Mathematical Analysis and Applications, 282 (1), 1-7. https://doi.org/10.1016/S0022-247X(03)00398-6