Abstract
LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for\(\overline {co} S = \overline {co} b(S)\) to hold is thatX have the following property (I): Every closed and bounded convex set is the intersection of a family of closed balls.
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Edelstein, M. Farthest points of sets in uniformly convex banach spaces. Israel J. Math. 4, 171–176 (1966). https://doi.org/10.1007/BF02760075
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DOI: https://doi.org/10.1007/BF02760075