Perturbation of Farthest Points in Weakly Compact Sets
Mathematica Moravica, Tome 15 (2011) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

If $f$ is a real valued weakly lower semi-continuous 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 $X$.
Mots-clés : Normed space, weakly compact set, farthest points 
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Jean-Matthieu Augé. Perturbation of Farthest Points in Weakly Compact Sets. Mathematica Moravica, Tome 15 (2011) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2011_15_1_a0/