Department of Applied Mathematics, Changwon National University, Changwon 641-773, Republic of Korea
Academic Editor: L. Górniewicz
Copyright © 2010 Jeong Sheok Ume. 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 first introduce the new concept of a distance called -distance, which generalizes -distance, Tataru's distance, and -distance. Then we prove
a new minimization theorem and a new fixed point theorem by using a -distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.