We introduce the concepts of ordered variational inequalities and ordered complementarity problems with both domain and range in Banach lattices. Then we apply the Fan-KKM theorem and KKM mappings to study the solvability of these problems.
"Ordered Variational Inequalities and Ordered Complementarity Problems in Banach Lattices." Abstr. Appl. Anal. 2013 (SI60) 1 - 9, 2013. https://doi.org/10.1155/2013/323126