Tripled fixed point theorems in cone metric spaces under F -invariant set and c -distance

Abstract

The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of F -invariant sets denoted by M in case of M ∈ X 6 in cone and ordered cone version. we also establish some tripled fixed point theorems in cone metric spaces under the concept of an F -invariant set for mappings F : X 3 → X and c-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.