Tian, Guoqiang and Zhou, Jianxin (1990): Quasivariational Inequalities with Noncompact Sets. Published in: Journal of Mathematical Analysis and Applications , Vol. 160, (1991): pp. 583595.

PDF
MPRA_paper_41230.pdf Download (535kB)  Preview 
Abstract
In this paper, we first generalize a foundational quasivariational inequality (Theorem 3) which plays a key role throughout this paper by relaxing the compactness condition. Then we set up general forms of (generalized) quasivariational inequalities and obtain a series of existence theorems without the compactness assumption. Also, since many other quasivariational inequalities in the literature are special cases of ours, they can be generalized by our results.
Item Type:  MPRA Paper 

Original Title:  Quasivariational Inequalities with Noncompact Sets 
Language:  English 
Keywords:  Quasivariational Inequalities; Noncompact Sets 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement 
Item ID:  41230 
Depositing User:  Guoqiang Tian 
Date Deposited:  12 Sep 2012 12:56 
Last Modified:  09 Apr 2017 08:49 
References:  1. G. Allen, Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. Appl. 58 (1977), 110. 2. K. Arrow and G. Debreu, Existence of equilibrium for a competitive economy, Econometrica 22 (1954), 265290. 3. J.P. Aubin, “Mathematical Methods of Game and Economic Theory,” NorthHolland, 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. 103113, Academic Press, New York, 1972. 7. K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519537. 8. U. Mosco, Implicit variational problems and quasivariational inequalities, in “Lecture Notes in Math.,” Vol. 543, pp. 83156, SpringerVerlag, New York/Berlin, 1976. 9. J. Nash, Equilibrium points in Nperson games, Proc. Natl. Acad. Sci. U.S.A. 36 (1950), 4849. 10. W. Shafer and H. Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), 345348. 11. M. H. Shin and K. K. Tan, Generalized quasivariational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl. 108 (1985), 333343. 12. W. Takahshi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 477481. 13. E. Tarafdar, A fix point theorem equivalent to the FanKnasterKuratowskiMazurkiewicz theorem, J. Math. Anal. Appl. 128 (1987), 475479. 14. G. Tian, Minimax inequalities equivalent to the FanKnasterKuratowskiMazurkiewicz theorems, to appear. 15. G. Tian, Equilibrium in abstract economies with a noncompact 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 noncompact and nonconvex domains, J. Math. Anal. Appl., in press. 17. J.X. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasivariational inequalities, J. Math. Anal. Appl. 132 (1988), 213225. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/41230 