A fixed point theorem in orbitally complete partially ordered metric spaces (Q472516)

Summary: Let \((X, \preceq)\) be a partially ordered set and \(T : X \to X\) 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 \textit{B. Samet} et al. [Fixed Point Theory Appl. 2013, Article ID 5, 11 p. (2013; Zbl 1285.54043)] to partially ordered sets. Also, we generalize the results of \textit{A. C. M. Ran} and \textit{M. C. B. Reurings} [Proc. Am. Math. Soc. 132, No.~5, 1435--1443 (2004; Zbl 1060.47056)].