A study of variational inequalities for set-valued mappings. (English) Zbl 0928.47045

Tan, Kok-Keong; Tarafdar, Enayet; Yuan, George Xian-Zhi

J. Inequal. Appl. 3, No. 2, 161-181 (1999).

Summary: 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 semicontinuous.

MSC:

47J20	Variational and other types of inequalities involving nonlinear operators (general)
47H04	Set-valued operators
47H05	Monotone operators and generalizations
47H10	Fixed-point theorems
49J40	Variational inequalities
52A07	Convex sets in topological vector spaces (aspects of convex geometry)

Keywords:

KKM mapping principle; simultaneous variational inequalities; Fan-Glicksberg fixed point theorem; implicit variational inequalities; set-valued mappings