Geodesic
Renormings of \(c_0\) and the minimal displacement problem
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2.

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The aim of this paper is to show that for every Banach space (X, ·) containing asymptotically isometric copy of the space c_0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with x - Tx 1 − 1/k for any x ∈ C. 
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Piasecki, Łukasz. Renormings of \(c_0\) and the minimal displacement problem. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2. http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a5/

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