Generalized Quasi-Variational-Like Inequality Problem

This paper gives some very general results on the generalized quasi-variational-like 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 selection-type arguments and thus is quite different from the Berge Maximum Theorem or Hahn-Banach Theorem approach used in the literature.

[1]  Jianxin Zhou,et al.  Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities , 1988 .

[2]  Quasi-variational Inequalities with Non-compact Sets , 1991 .

[3]  E. Peterson,et al.  Generalized variational inequalities , 1982 .

[4]  Romesh Saigal,et al.  Extension of the Generalized Complementarity Problem , 1976, Math. Oper. Res..

[5]  J. S. Pang,et al.  The Generalized Quasi-Variational Inequality Problem , 1982, Math. Oper. Res..

[6]  George L Allen,et al.  Variational inequalities, complementarity problems, and duality theorems , 1977 .

[7]  Zhang Cong-jun,et al.  Generalized variational inequalities and generalized quasi-variational inequalities , 1993 .

[8]  N. Yannelis Equilibria in noncooperative models of competition , 1987 .

[9]  D. Montgomery,et al.  Fixed Point Theorems for Multi-Valued Transformations , 1946 .

[10]  Nicholas C. Yannelis,et al.  Existence of Maximal Elements and Equilibria in Linear Topological Spaces , 1983 .

[11]  Jianxin Zhou,et al.  Quasi-Variational Inequalities without Concavity Assumptions , 1991 .

[12]  C. J. Himmelberg Fixed points of compact multifunctions , 1972 .

[13]  Guoqiang Tian,et al.  Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets , 1992, SIAM J. Optim..

[14]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[15]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[16]  Ying Zhang,et al.  Generalized KKM theorem and variational inequalities , 1991 .

[17]  U. Mosco Implicit variational problems and quasi variational inequalities , 1976 .

[18]  J. Parida,et al.  A variational-like inequality for multifunctions with applications , 1987 .

[19]  E. Michael Continuous Selections. I , 1956 .

[20]  Jen-Chih Yao,et al.  The generalized quasi-variational inequality problem with applications , 1991 .

[21]  Guoqiang Tian Fixed points theorems for mappings with non-compact and non-convex domains , 1991 .

[22]  Mau-Hsiang Shih,et al.  Generalized quasi-variational inequalities in locally convex topological vector spaces , 1985 .

[23]  B. Craven Invex functions and constrained local minima , 1981, Bulletin of the Australian Mathematical Society.

[24]  G. Stampacchia,et al.  On some non-linear elliptic differential-functional equations , 1966 .

[25]  Guoqiang Tian Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity , 1992 .

[26]  Olvi L. Mangasarian,et al.  Minmax and duality in nonlinear programming , 1965 .

[27]  T. Bergstrom,et al.  Preferences Which Have Open Graphs , 1976 .

[28]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .