On Vector Variational Inequalities in Reflexive Banach Spaces

In this paper, we study the solvability for a class of vector variational inequalities in reflexive Banach spaces. By using Brouwer fixed point theorem, we prove the solvability for this class of vector variational inequalities without monotonicity assumption. The solvability results for this class of vector variational inequalities with monotone mappings are also presented by using the KKM-Fan lemma

[1]  Xiaoqi Yang,et al.  Vector complementarity and minimal element problems , 1993 .

[2]  F. Giannessi,et al.  Variational inequalities and network equilibrium problems , 1995 .

[3]  G. Chen.  Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem , 1992 .

[4]  A. H. Siddiqi,et al.  On vector variational inequalities , 1995 .

[5]  Chen Guang-ya,et al.  The vector complementary problem and its equivalences with the weak minimal element in ordered spaces , 1990 .

[6]  G Chen.  VECTOR VARIATIONAL INEQUALITY AND ITS APPLICATION FOR MULTIOBJECTIVE OPTIMIZATION , 1989 .

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

[8]  Do Sang Kim,et al.  Generalized vector variational inequality , 1996 .

[9]  Jen-Chih Yao,et al.  On vector variational inequalities , 1996 .

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

[11]  Ky Fan,et al.  Some properties of convex sets related to fixed point theorems , 1984 .

[12]  Bruce D. Craven,et al.  A vector variational inequality and optimization over an efficient set , 1990, ZOR Methods Model. Oper. Res..

[13]  Xiaoqi Yang,et al.  On Vector Variational Inequalities: Application to Vector Equilibria , 1997 .

[14]  Xiaoqi Yang.  Vector Variational Inequality and Vector Pseudolinear Optimization , 1997 .

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

[16]  L. Brouwer.  Beweis der Invarianz desn-dimensionalen Gebiets , 1911 .

[17]  J. Y. Fu.  Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem , 1997 .

[18]  Xiaoqi Yang.  Vector variational inequality and its duality , 1993 .

[19]  Jen-Chih Yao,et al.  Existence Results for VVIP , 1996 .

[20]  Changyu Wang,et al.  Continuousization of the family of point-to-set maps and its applications , 1990 .