International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 196326, 6 pages
doi:10.1155/2008/196326
Farthest Points and Subdifferential in p-Normed Spaces
S. Hejazian
, A. Niknam
and S. Shadkam
Department of Mathematics and Center of Excellence in Analysis on Algebraic structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
Abstract
We study the farthest point mapping in a p-normed space X in virtue of subdifferential of r(x)=sup{‖x−z‖p:z∈M}, where M is a weakly sequentially compact subset of X. We show that the set of all points in X which have farthest point in M contains a dense Gδ subset of X.