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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 407219, 8 pages
http://dx.doi.org/10.1155/2013/407219
Research Article

On Caristi Type Maps and Generalized Distances with Applications

Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Received 3 July 2013; Accepted 5 August 2013

Academic Editor: E. Karapinar

Copyright © 2013 Wei-Shih Du. 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 prove some new existence theorems of fixed points for Caristi type maps and some suitable generalized distances without lower semicontinuity assumptions on dominated functions. As applications of our results, some new fixed point theorems and new generalizations of the Banach contraction principle are given.