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.

Publication Title

Journal of Mathematical Analysis and Applications