Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 397150, 21 pages
doi:10.1155/2010/397150
Research Article

Existence Theorems for Generalized Distance on Complete Metric Spaces

Jeong Sheok Ume

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

Received 20 September 2009; Revised 7 May 2010; Accepted 20 May 2010

Academic Editor: L. Górniewicz

Copyright © 2010 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.

Abstract

We first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.