This is an announcement for the paper "Perturbation of farthest points in weakly compact sets" by Jean-Matthieu Auge.

Abstract: If $f$ is a real valued weakly lower semi-continous function on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show that the set of $x \in X$ such that $z \mapsto |x-z|-f(z)$ attains its supremum on $C$ is dense in $X$. We also construct a counter example showing that the set of $x \in X$ such that $z \mapsto |x-z|+|z|$ attains its supremum on $C$ is not always dense in $X$.

Archive classification: math.FA

Mathematics Subject Classification: Primary 41A65

Remarks: 5 pages

Submitted from: jean-matthieu.auge@math.u-bordeaux1.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.2047

or

http://arXiv.org/abs/1204.2047