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.


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
Full Text: DOI


[1] DOI: 10.1006/jmaa.1996.0406 · Zbl 0867.49008
[2] DOI: 10.1007/BF00940305
[3] DOI: 10.1016/0304-4068(76)90016-1 · Zbl 0349.90157
[4] Bianchi, Pseudo P-monotone operators and variational inequalities 6 (1993)
[5] DOI: 10.1016/0304-4068(83)90041-1 · Zbl 0536.90019
[6] DOI: 10.1006/jmaa.1996.0007 · Zbl 0852.54019
[7] DOI: 10.1137/S1052623494250415 · Zbl 0855.47043
[8] DOI: 10.1090/S0002-9939-97-03903-8 · Zbl 0871.47038
[9] DOI: 10.1007/BF01472256 · Zbl 0012.30803
[10] DOI: 10.1016/S0362-546X(96)00142-3 · Zbl 0912.49004
[11] DOI: 10.1007/BF02591749 · Zbl 0578.49006
[12] DOI: 10.2307/2041249 · Zbl 0369.47029
[13] DOI: 10.1090/S0002-9939-98-04347-0 · Zbl 0891.46004
[14] DOI: 10.1007/BF01353421 · Zbl 0093.36701
[15] Ding, Bull. Austral. Math. Soc. 46 pp 205– (1992)
[16] DOI: 10.1007/BF01350721 · Zbl 0176.45204
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