On -compatible mappings and common coupled coincidence point in cone metric spaces

Recently, Abbas et al. [M. Abbas, M.A. Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w -compatible mapping, Applied Mathematics and Computation (2010) doi:10.1016/j.amc.2010.05.042] introduced the concept of w -compatible mappings and obtained results on coupled coincidence point for nonlinear contractive mappings in a cone metric space. In the present paper, we introduce the concept of a common coupled coincidence point of the mappings F , G : X × X → X and f : X → X and we prove some theorems for nonlinear contractive mappings in a cone metric space with a cone having nonempty interior. Our results generalize several well known comparable results in the literature.