Abstract
We characterise the relative Chebyshev centre of a compact subsetFof a real Banach space in terms of the Gateaux derivative of the distance to farthest points. We present a relative-Chebyshev-centre characterisation of Hilbert space. In Hilbert space we show that the relative Chebyshev centre is in the closed convex hull of the metric projection ofF, and we estimate the relative Chebyshev radius ofF.
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