Convexities and Existence of the Farthest Point

Z. H. Zhang and C. Y. Liu

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: Five counterexamples are given, which show relations among the new convexities and some important convexities in Banach space. Under the assumption that Banach space X is nearly very convex, we give a sufficient condition that bounded, weakly closed subset of X has the farthest points. We also give a sufficient condition that the farthest point map is single valued in a residual subset of X when X is very convex.

Date: 2011
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https://doi.org/10.1155/2011/139597

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:139597

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