The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.

[1]  F. Giannessi.  Vector Variational Inequalities and Vector Equilibria , 2000 .

[2]  Jen-Chih Yao,et al.  On Nondifferentiable and Nonconvex Vector Optimization Problems , 2000 .

[3]  Werner Oettli,et al.  Generalized vectorial equilibria and generalized monotonicity , 1998 .

[4]  Wen Song,et al.  Vector Equilibrium Problems with Set-Valued Mappings , 2000 .

[5]  Jen-Chih Yao,et al.  System of Vector Equilibrium Problems and Its Applications , 2000 .

[6]  Nicolas Hadjisavvas,et al.  Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems , 1998 .

[7]  B. D. Craven,et al.  Nondifferentiable optimization by smooth approximations , 1986 .

[8]  Siegfried Schaible,et al.  From Scalar to Vector Equilibrium Problems in the Quasimonotone Case , 1998 .

[9]  Ouayl Chadli,et al.  On Generalized Vector Equilibrium Problems , 2000, J. Glob. Optim..

[10]  G. Lee,et al.  On vector quasivariational inequalities , 1996 .

[11]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[12]  Xie Ping Ding,et al.  GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES WITHOUT MONOTONICITY , 2000 .

[13]  Jen-Chih Yao,et al.  Systems of generalized variational inequalities and their applications , 2000 .

[14]  Jen-Chih Yao,et al.  A fixed point theorem and its applications to a system of variational inequalities , 1999, Bulletin of the Australian Mathematical Society.

[15]  Tan Nguyen Xuan,et al.  On the existence of equilibrium points of vector functions , 1998 .

[16]  S. Schaible,et al.  Vector Equilibrium Problems with Generalized Monotone Bifunctions , 1997 .

[17]  C. Tammer,et al.  Theory of Vector Optimization , 2003 .

[18]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[19]  Jen-Chih Yao,et al.  An existence result for the generalized vector equilibrium problem , 1999 .

[20]  Qamrul Hasan Ansari,et al.  A generalization of vectorial equilibria , 1997, Math. Methods Oper. Res..

[21]  Werner Oettli,et al.  Existence of equilibria for monotone multivalued mappings , 1998, Math. Methods Oper. Res..

[22]  Jen-Chih Yao,et al.  On the Generalized Vector Variational Inequality Problem , 1997 .

[23]  G. M. Lee,et al.  On Implicit Vector Variational Inequalities , 2000 .

[24]  S. Semmes.  Topological Vector Spaces , 2003 .

[25]  George Xian-Zhi Yuan,et al.  The study of maximal elements, fixed points for LS-majorized mappings and their applications to minimax and variational inequalities in product topological spaces☆ , 1999 .

[26]  W. Oettli.  A remark on vector-valued equilibria and generalized monotonicity , 1997 .

[27]  Nicolas Hadjisavvas,et al.  Existence theorems for vector variational inequalities , 1996, Bulletin of the Australian Mathematical Society.

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

[29]  Q. H. ANSARI,et al.  On Nondifferentiable and Nonconvex Vector Optimization Problems 1 , 2000 .

[30]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .