Existence On The Common Fixed Point And The Coupled Coincidence Point For Expansive Maps In Cone B-metric Spaces

In this paper, the author mainly studies the existence on the common fixed point, and the coupled coincidence point for two expansive maps in cone b- metric spaces. The author put forward some new concepts, and remove the continuity conditions which are generally assumed in the literatures. Under the weaker conditions, we give the existence results. The results obtained extend some relevant conclusions in the recent literatures. The paper includes four chapters as follows:In the first chapter, as an introduction, the author mainly introducs the background of expansive type maps on cone b- metric spaces and the present situation, as well as the composition, main contents and conclusions.In the second chapter, some of expansive maps of the metric spaces and the cone metric spaces of two expansive maps have been extended to the cone b- metric spaces, and the results on existence of common fixed points are established. With respect to the recent literatures, the results we obtained, on the one hand generalize the expansive conditions in some literatures, on the other hand remove the continuity conditions which are generally given in the literatures.In the third chapter, the author puts forward an new expansive map in cone b-metric space. Based on the definition of coupling coincidence point, we introduce a definition of strong coupled coincidence point. Under the weaker conditions, the author proves the existence of the strong form of coupled coincidence point in cone b- metric spaces.In the fourth chapter, we have a conclusion, and we give some directions which we need to study later.