A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces

Abstract EN

Let (X,⪯) be a partially ordered set and T:X→X be a mapping.

We prove a fixed point theorem for the map T satisfying a contractive condition in orbits, when X is T-orbitally complete.

Our result extends and generalizes the results of Samet et al.

(2013) to partially ordered sets.

Also, we generalize the results of Ran and Reurings (2004).