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

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)
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