Set-valued versions of Ky Fan's inequality with application to variational inclusion theory

In this paper, we prove two set-valued versions of Ky Fan's minimax inequality. From these results, versions of Schauder's and Kakutani's fixed point theorems can be deduced. We formulate a variational inclusion problem for set-valued maps and a differential inclusion problem, concerning the contingent derivative. Sufficient conditions for the existence of solution for these inclusion problems are obtained, generalizing classical variational inequality problems.