Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 230101, 15 pages
Research Article

Extensions of Minimization Theorems and Fixed Point Theorems on a Quasimetric Space

Jeong Sheok Ume

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

Received 16 March 2008; Accepted 9 June 2008

Academic Editor: Thomas Bartsch

Copyright © 2008 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 introduce the new concepts of e-distance, e-type mapping with respect to some e-distance and S-complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an S-complete quasimetric space. We also give some examples of quasimetrics, e-distances, and e-type mapping with respect to some e-distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others.