Coupled fixed point results in cone metric spaces for w-compatible mappings

Abstract

In this paper, we introduce the concepts of w-compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F,G : X x X -> X, where (X, d) is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered.