Coincidence points principle for set-valued mappings in partially ordered spaces

In the paper the concept of covering (regularity) for set-valued mappings in partially ordered spaces is introduced. The coincidence points problem for set-valued mappings in partially ordered spaces is considered. Sufficient conditions for the existence of coincidence points of isotone and orderly covering set-valued mappings are obtained. It is shown that the known theorems on coincidence points of covering and Lipschitz mappings in metric spaces can be deduced from the obtained results.