Tian, Guoqiang (1991): Generalized quasivariationallike inequality problem. Published in: Mathematics of Operations Research , Vol. 18, No. 3 (August 1993): pp. 752764.

PDF
MPRA_paper_41219.pdf Download (944kB)  Preview 
Abstract
This paper gives some very general results on the generalized quasivariationallike inequality problem. Since the problem includes all the existing extensions of the classical variational inequality problem as special cases, our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional. The approach adopted in this paper is based on continuous selectiontype arguments and thus is quite different from the Berge Maximum Theorem or HahnBanach Theorem approach used in the literature.
Item Type:  MPRA Paper 

Original Title:  Generalized quasivariationallike inequality problem 
Language:  English 
Keywords:  QuasiVariational; Inequality; Problem 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement 
Item ID:  41219 
Depositing User:  Guoqiang Tian 
Date Deposited:  13 Sep 2012 22:45 
Last Modified:  10 Oct 2016 22:10 
References:  [1] Allen, G. (1977). Variational Inequalities, Complementarity Problems, and Duality Theorems, J. Math. Anal. Appl. 58 110. [2] Arrow, K. and Debreu, G. (1954). Existence of Equilibrium for a Competitive Economy. Economet rica 22 265290. [3] Aubin, J. P. (1979). Mathematical Methods of Game and Economic Theory. NorthHolland, Amster dam, Holland. [4] Ekeland, I. (1984). Applied Nonlinear Analysis. John Wiley & Sons, New York. [5] Bergstrom, T. C., Parks, R. P. and Rader, T. (1976). Preferences Which Have Open Graphs. J. Math. Econom. 3 265268. [6] Chan, D. and Pang, J. S. (1982). The Generalized QuasiVariational Inequality Problem. Math. Oper. Res. 7 211222. [7] Chang, S. and Zhang, Y. (1991). Generalized KKM Theorem and Variational Inequalities. J. Math. Anal. Appl. 159 208223. [8] Craven, B. D. (1981). Invex Functions and Constrained Local Minima. Bull. Austral. Math. Soc. 24 357366. [9] Debreu, G. (1952). A Social Equilibrium Existence Theorem. Proc. Nat. Acad. Sci. U.S.A. 38 386393. [10] Ding, X. P. and Tan, K.K. (1990). Generalized Variational Inequalities and Generalized QuasiVari ational Inequalities. J. Math. Anal. Appl. 148 497508. [11] Eilenberg, S. and Montgomery, D. (1946). Fixed Point Theorems for MultiValued Transformations. Amer. J. Math. 68 214222. [12] Fang, S. C. and Peterson, E. L. (1982). Generalized Variational Inequalities. J. Optim. Theory Appl. 38 363383. [13] Hanson, M. A. (1981). On Sufficiency of the KuhnTucker Conditions. J. Math. Anal. Appl. 80 545550. [14] Hartman, P. T. and Stampacchia, G. (1966). On Some Nonlinear Ecliptic Differential Functional Equations. Acta Math. 115 153188. [15] Himmelberg, C. J. (1972). Fixed Points of Compact Multifunctions. J. Math. Anal. Appl. 38 205207. [16] Mangasarian, O. L. and Ponstein, J. (1965). Minimax and Duality in Nonlinear Programming. J. Math. Anal. Appl. 11 504518. [17] Michael, E. (1956). Continuous Selections. I. Ann. of Math. (2) 63 361382. [18] Mosco, U. (1976). Implicit Variational Problems and QuasiVariational Inequalities. in Lecture Notes in Math. Vol. 543, 83156, Springer Verlag, New York/Berlin. [19] Parida, J. and Sen, A. (1987). A VariationalLike Inequality for Multifunctions with Applications. J. Math. Anal. Appl. 124 7381. [20] Saigal, R. (1976). Extension of the Generalized Complementarity Problem. Math. Oper. Res. 1 260266. [21] Shih, M. H. and Tan, K. K. (1985). Generalized QuasiVariational Inequalities in Locally Convex Topological Vector Spaces. J. Math. Anal. Appl. 108 333343. [22] Tian, G. (1991). Fixed Points Theorems for Mappings with Noncompact and Nonconvex Domains. J. Math. Anal. Appl. 158 160167. [23] (1992). Existence of Equilibrium in Abstract Economies with Discontinuous Payoffs and Noncompact Choice Spaces. J. Math. Econom. 21 379388. [24] (1992). Generalizations of the FKKM Theorem and KyFan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity. J. Math. Anal. Appl. 170 457471. [25] and Zhou, J. (1991). QuasiVariational Inequalities with Noncompact Sets. J. Math. Anal. Appl. 160 583595. [26] Tian, G. (1991) and Zhou, J. (1993). QuasiVariational Inequalities without Concavity Assumption Math. Anal. Appl. 172 289299. [27] Yannelis, N. C. (1987). Equilibria in Noncooperative Models of Competition. J. Econom. Theory 96111. [28] and Prabhakar, N. D. (1983). Existence of Maximal Elements and Equilibria in Lin Topological Spaces. J. Math. Econom. 12 233245. [29] Yao, J. C. (1991). The Generalized QuasiVariational Inequality with Applications. J. Math. An Appl. 158 139160. [30] Zhou, J. X. and G. Chen, (1988). Diagonal Convexity Conditions for Problems in Convex Analy and QuasiVariational Inequalities. J. Math. Anal. Appl. 132 213225. [31] and Tian, G. (1992). Transfer Method for Characterizing the Existence of Maximal Eleme of Binary Relations on Compact or Noncompact Sets. SIAM J. Control Optim. 2 360375. G. Tian: Department of Economics, Texas A&M University, College Station, Texas 77843 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/41219 