On Coincidence and Common Fixed Points for Compatible Hybrid Mappings in Partial Metric Spaces Related to Partial Order

In this paper, we prove the existence of coincidence points for hybrid mapping pairs and their common fixed points by utilizing the compatibility properties. Our new results extend the theorems on coincidence points and common fixed points of compatible hybrid mapping pairs in partial metric spaces under partial ordering. Additionally, we establish new theorems on coincidence and common fixed points in partially ordered sets. Some illustrative examples are also provided.