International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 7, Pages 443-447

A minimization theorem in quasi-metric spaces and its applications

Jeong Sheok Ume

Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea

Received 25 October 2001

Copyright © 2002 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 prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland's ϵ-variational principle.