×
Ansari, Qamrul Hasan; Yao, Jen-Chih

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

Bull. Aust. Math. Soc. 59, No. 3, 433-442 (1999).
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.

Cited in 1 Review
Cited in 106 Documents

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

Keywords:

fixed point theorem; multivalued maps defined on product spaces; equilibrium existence theorem; abstract economy; variational inequalities
PDF BibTeX XML Cite
\textit{Q. H. Ansari} and \textit{J.-C. Yao}, Bull. Aust. Math. Soc. 59, No. 3, 433--442 (1999; Zbl 0944.47037)
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.