Open Access

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

Fixed Point Theory and Applications20082008:230101

Received: 16 March 2008

Accepted: 9 June 2008

Published: 12 June 2008


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.

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Authors’ Affiliations

Department of Applied Mathematics, Changwon National University


© Jeong Sheok Ume. 2008

This article is published under license to BioMed Central Ltd. 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.