convexities and existence of the farthest point
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ID: 183670
2011
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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 ๐ is nearly very convex, we give a sufficient
condition that bounded, weakly closed subset of ๐ has the farthest points. We also give a sufficient condition that the farthest point map is single valued in a
residual subset of ๐ when ๐ is very convex.
| Reference Key |
zhang2011abstractconvexities
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|---|---|
| Authors | ;Z. H. Zhang;C. Y. Liu |
| Journal | science and technology of advanced materials |
| Year | 2011 |
| DOI |
10.1155/2011/139597
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| URL | |
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