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Fixed points of isometries on weakly compact convex sets

✍ Scribed by Teck-Cheong Lim; Pei-Kee Lin; C. Petalas; T. Vidalis

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 76 KB
Volume: 282
Category: Article
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00398-6

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✦ Synopsis

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 isometries from a nonempty bounded closed convex subset of a uniformly convex Banach space into itself have the Chebyshev center as a common fixed point.

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