Common Fixed Points In Cone Metric Spaces For \(MK\)-Pairs And \(L\)-Pairs

Abstract

In this paper, we introduce some contractive conditions of Meir-Keeler type for a pair of mappings, called MK-pair and L-pair, in the framework of cone metric spaces. We prove theorems which assure the existence and uniqueness of common fixed points for MK-pairs and L-pairs. As an application, we obtain a result on the common fixed point of a p-MK-pair, a mapping, and a multifunction in complete cone metric spaces. These results extend and generalize well-known comparable results in the literature.