Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 230101, 15 pages
Extensions of Minimization Theorems and Fixed Point Theorems on a Quasimetric Space
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 -distance, -type mapping with respect to some -distance and -complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an -complete quasimetric space. We also give some examples of quasimetrics, -distances, and -type mapping with respect to some -distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others.