A study of variational inequalities for set-valued mappings

Abstract

In this paper, Ky Fan's KKM mapping principle is used to establish the existence of solutions for simultaneous variational inequalities. By applying our earlier results together with Fan–Glicksberg fixed point theorem, we prove some existence results for implicit variational inequalities and implicit quasi-variational inequalities for set-valued mappings which are either monotone or upper semi-continuous.

Keywords

• Monotone pair
• Simultaneous variational inequality
• KKM mapping principle
• Fan–Glicksberg fixed point theorem
• Implicit quasi-variational inequality