In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.
"Fixed Point Theorems of Set-Valued Mappings in Partially Ordered Hausdorff Topological Spaces." Abstr. Appl. Anal. 2014 (SI05) 1 - 5, 2014. https://doi.org/10.1155/2014/232413