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A fixed point theorem and its applications to a system of variational inequalities. (English) Zbl 0944.47037

Summary: We first prove a fixed point theorem for a family of multivalued maps defined on product spaces. We then apply our result to prove an equilibrium existence theorem for an abstract economy. We also consider a system of variational inequalities and prove the existence of its solutions by using our fixed point theorem.

MSC:

47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
47H04 Set-valued operators
91B50 General equilibrium theory
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