Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem

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. Copyright (C) 2009 T. Abdeljawad and E. Karapinar.