Convexities and Existence of the Farthest Point

Z. H. Zhang, C. Y. Liu
2011 Abstract and Applied Analysis  
Five counterexamples are given, which show relations among the new convexities and some important convexities in Banach space. Under the assumption that Banach space is nearly very convex, we give a sufficient condition that bounded, weakly closed subset of has the farthest points. We also give a sufficient condition that the farthest point map is single valued in a residual subset of when is very convex.
doi:10.1155/2011/139597 fatcat:bg2zvv3mevh2foj45vj3qbqcji