# Article

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Keywords:
renormings; non-reflexive Banach spaces; Chebyshev centers
Summary:
Let $X$ be a non-reflexive real Banach space. Then for each norm $|\cdot|$ from a dense set of equivalent norms on $X$ (in the metric of uniform convergence on the unit ball of $X$), there exists a three-point set that has no Chebyshev center in $(X,|\cdot|)$. This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin.
References:
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