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International Journal of Mathematics and Mathematical Sciences 
Volume 31 (2002), Issue 7, Pages 443-447
doi:10.1155/S0161171202110404

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

Abstract

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.