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International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 196326, 6 pages
Research Article

Farthest Points and Subdifferential in 𝑝 -Normed Spaces

Department of Mathematics and Center of Excellence in Analysis on Algebraic structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran

Received 25 December 2007; Revised 9 March 2008; Accepted 13 March 2008

Academic Editor: Narendra Kumar Govil

Copyright © 2008 S. Hejazian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the farthest point mapping in a 𝑝 -normed space 𝑋 in virtue of subdifferential of π‘Ÿ ( π‘₯ ) = s u p { β€– π‘₯ βˆ’ 𝑧 β€– 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 𝐺 𝛿 subset of 𝑋 .