"Fixed points of isometries on weakly compact convex sets" by Teck Cheong Lim, Pei Kee Lin et al.
 

Fixed points of isometries on weakly compact convex sets

Abstract

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

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