Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 574387, 9 pages
doi:10.1155/2009/574387
Research Article

Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem

Thabet Abdeljawad1 and Erdal Karapinar2

1Department of Mathematics, Çankaya University, 06530 Ankara, Turkey
2Department of Mathematics, Atılım University, 06836 Ankara, Turkey

Received 4 July 2009; Accepted 3 December 2009

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2009 Thabet Abdeljawad and Erdal Karapinar. 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

Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik's fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces.