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Zbl 0944.47037
Ansari, Qamrul Hasan; Yao, Jen-Chih
A fixed point theorem and its applications to a system of variational inequalities. (English)
[J] Bull. Aust. Math. Soc. 59, No.3, 433-442 (1999). ISSN 0004-9727

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 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J20 Inequalities involving nonlinear operators
49J40 Variational methods including variational inequalities
47H04 Set-valued operators
91B50 Equilibrium in economics

Keywords: fixed point theorem; multivalued maps defined on product spaces; equilibrium existence theorem; abstract economy; variational inequalities

Cited in: Zbl 1218.49013

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Zentralblatt MATH Berlin [Germany]