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