Tian, Guoqiang and Zhou, Jianxin (1990): Quasi-variational Inequalities with Non-compact Sets. Published in: Journal of Mathematical Analysis and Applications , Vol. 160, (1991): pp. 583-595.
Download (535kB) | Preview
In this paper, we first generalize a foundational quasi-variational inequality (Theorem 3) which plays a key role throughout this paper by relaxing the compactness condition. Then we set up general forms of (generalized) quasi-variational inequalities and obtain a series of existence theorems without the compactness assumption. Also, since many other quasi-variational inequalities in the literature are special cases of ours, they can be generalized by our results.
|Item Type:||MPRA Paper|
|Original Title:||Quasi-variational Inequalities with Non-compact Sets|
|Keywords:||Quasi-variational Inequalities; Non-compact Sets|
|Subjects:||D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement|
|Depositing User:||Guoqiang Tian|
|Date Deposited:||12 Sep 2012 12:56|
|Last Modified:||28 Apr 2016 08:11|
1. G. Allen, Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. Appl. 58 (1977), 1-10.
2. K. Arrow and G. Debreu, Existence of equilibrium for a competitive economy, Econometrica 22 (1954), 265-290.
3. J.P. Aubin, “Mathematical Methods of Game and Economic Theory,” North-Holland, Amsterdam, 1979.
4. J.P. Aubin and I. Ekeland, “Applied Nonlinear Analysis,” Wiley, New York, 1984.
5. G. Debreu, A social equilibrium existence theorem, Proc. Natl. Acad. Sci. U.S.A. 38 (1952).
6. K. Fan, A minimax inequality and applications, in “inequalities” (O. Shisha, Ed.), Vol.3, pp. 103-113, Academic Press, New York, 1972.
7. K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537.
8. U. Mosco, Implicit variational problems and quasi-variational inequalities, in “Lecture Notes in Math.,” Vol. 543, pp. 83-156, Springer-Verlag, New York/Berlin, 1976.
9. J. Nash, Equilibrium points in N-person games, Proc. Natl. Acad. Sci. U.S.A. 36 (1950), 48-49.
10. W. Shafer and H. Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), 345-348.
11. M. H. Shin and K. K. Tan, Generalized quasi-variational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl. 108 (1985), 333-343.
12. W. Takahshi, Non-linear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 477-481.
13. E. Tarafdar, A fix point theorem equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem, J. Math. Anal. Appl. 128 (1987), 475-479.
14. G. Tian, Minimax inequalities equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorems, to appear.
15. G. Tian, Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences, Econom. Lett., in press.
16. G. Tian, Fixed points theorems for mappings with non-compact and non-convex domains, J. Math. Anal. Appl., in press.
17. J.X. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities, J. Math. Anal. Appl. 132 (1988), 213-225.