Journal of Applied Mathematics
Volume 2013 (2013), Article ID 527417, 5 pages
Note on the Hahn-Banach Theorem in a Partially Ordered Vector Space
1College of Engineering, Nihon University, Naka-gawara, Tokusada, Tamura-machi, Koriyama-shi, Fukushima 963-8642, Japan
2Faculty of Engineering, Tamagawa University, 6-1-1 Tamagawa-gakuen, Machida-shi, Tokyo 194-8610, Japan
3Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan
Received 17 May 2013; Accepted 25 June 2013
Academic Editor: Wei-Shih Du
Copyright © 2013 Toshiharu Kawasaki 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.
Using a fixed point theorem in a partially ordered
set, we give a new proof of the Hahn-Banach theorem in the case where the
range space is a partially ordered vector space.