Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property
1 Department of Mathematics, Texas A&M University Kingsville, Kingsville, TX, 78363, USA
2 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
3 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Kru, Bangkok, 10140, Thailand
Fixed Point Theory and Applications 2013, 2013:22 doi:10.1186/1687-1812-2013-22Published: 31 January 2013
In this paper, we prove the coupled coincidence point theorems for a -compatible mapping in partially ordered cone metric spaces over a solid cone without the mixed g-monotone property. In the case of a totally ordered space, these results are automatically obvious under the assumption given. Therefore, these results can be applied in a much wider class of problems. We also prove the uniqueness of a common coupled fixed point in this setup and give some example which is not applied to the existence of a common coupled fixed point by using the mixed g-monotone property but can be applied to our results.
MSC: 47H10, 54H25.