The notion of $(X, \preceq)$ partially ordered set is well known and its study for fixed points is well entrenched in the literature. In this manuscript, we obtain sufficient conditions for the existence of common fixed point for two set valued mappings satisfying an implicit relation in complete $G$-metric space on partially ordered set $X$.
"Fixed point theorems for set valued mappings in partially ordered $G$-metric space." Tbilisi Math. J. 7 (1) 45 - 54, 2014. https://doi.org/10.2478/tmj-2014-0005