Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings
Duran TURKOGLU1, Muhib ABULOHA2
1. Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar,Ankara 06500, Turkey;
2. Department of Mathematics, Institute of Science and Technology, Gazi University,Ankara 06500, Turkey
Abstract In this paper, some topological concepts and definitions are generalized to cone metricspaces. It is proved that every cone metric space is first countable topological space and that sequentiallycompact subsets are compact. Also, we define diametrically contractive mappings and asymptoticallydiametrically contractive mappings on cone metric spaces to obtain some fixed point theorems byassuming that our cone is strongly minihedral.