Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 230101, 15 pages
doi:10.1155/2008/230101

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

Abstract

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.