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.
Shujun Jiang. Zhilong Li. Shihua Luo. "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