Fixed Points for Contraction Mappings in Generalized Cone Metric Spaces

Abstract

We prove in this paper several fixed point results for mappings that satisfy certain contractive conditions in generalized cone metric spaces. Importantly, our results generalize, extend, and unify some other results in the literature in the sense that they are analogous to those for cone metric spaces, but in a more general setting, where we have here G-cone metric spaces, or in the sense that they are extension or generalization of some other results proved previously in G-metric spaces.

Key words and phrases. Generalized metric space, cone metric space, fixed point.

2000 Mathematics Subject Classification. 47H10, 54H25, 54E35, 46B20