Journal of Applied Mathematics
Volume 2013 (2013), Article ID 527417, 5 pages
http://dx.doi.org/10.1155/2013/527417
Research Article

Note on the Hahn-Banach Theorem in a Partially Ordered Vector Space

Toshiharu Kawasaki,1 Masashi Toyoda,2 and Toshikazu Watanabe3

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.

Abstract

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.