System of generalised set-valued quasi-variational-like inequalities

In this paper, we shall introduce a system of generalised set-valued quasi-variational-like inequalities, which generalises and unifies systems of generalised vector variational inequalities, systems of variational inequalities, generalised vector quasi-variational-like inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence results for a solution of a system of generalized set-valued quasi-variational-like inequalities without any monotonity are obtained.

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

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

[3]  X. Ding.  Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings , 1997 .

[4]  Xiaoqi Yang,et al.  Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities , 2002 .

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

[6]  Jong-Shi Pang,et al.  Asymmetric variational inequality problems over product sets: Applications and iterative methods , 1985, Math. Program..

[7]  Jen-Chih Yao,et al.  Generalized Vector Variational Inequalities , 1997 .

[8]  Qamrul Hasan Ansari,et al.  Extended generalized vector variational-like inequalities for nonmonotone multivalued maps , 1997 .

[9]  X. Ding.  The generalized vector quasi-variational-like inequalities☆ , 1999 .

[10]  E. Michael.  A note on paracompact spaces , 1953 .

[11]  Qamrul Hasan Ansari,et al.  A Note On Generalized Vector Variational-Like Inequalities , 1997 .

[12]  S. J. Li,et al.  Existence of solutions for a generalized vector quasivariational inequality , 1996 .

[13]  V. Sehgal,et al.  Some fixed point theorems for condensing multifunctions in locally convex spaces , 1975 .

[14]  Guoqiang Tian,et al.  Quasi-Variational Inequalities without the Concavity Assumption , 1993 .

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

[16]  Xiaoqi Yang,et al.  Generalized convex functions and vector variational inequalities , 1993 .

[17]  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.

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

[19]  Gue Myung Lee,et al.  ON VECTOR VARIATIONAL INEQUALITY , 1996 .

[20]  B. D. Craven,et al.  Approximate dual and approximate vector variational inequality for multiobjective optimization , 1989, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

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

[22]  G. Cohen,et al.  Nested monotony for variational inequalities over product of spaces and convergence of iterative algorithms , 1988 .

[23]  D. Mayne.  Nested Monotony for Variational Inequalities over Product of Spaces and Convergence of Iterative Algorithms , 1988 .

[24]  Guang-Ya Chen,et al.  Vector Variational Inequality and Vector Optimization Problem , 1987 .

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

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

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

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

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

[30]  K. Fan.  Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

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

[32]  Luo Qun.  Generalized Vector Variational-Like Inequalities , 2000 .

[33]  Elisabetta Allevi,et al.  Generalized vector variational inequalities over product sets , 2001 .

[34]  Do Sang Kim,et al.  Generalized vector variational inequality and fuzzy extension , 1993 .

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

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

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

[38]  J. Aubin,et al.  Applied Nonlinear Analysis , 1984 .

[39]  Xian-Zhi Yuan,et al.  Generalized quasi-variational inequalities and some applications , 1997 .

[40]  Xie Ping Ding,et al.  Generalized Vector Variational-Like Inequalities with Cx - η-Pseudomonotone Set-Valued Mappings , 2000 .

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

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

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

[44]  Existence of solutions for generalized quasi-variational-like inequalities , 1997 .