A vector version of Minty's Lemma and application

Abstract In this paper, we consider a vector version of Minty's Lemma and obtain existence theorems for two kinds of vector variational-like inequalities.

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

[2]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

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

[4]  F. Giannessi On Minty Variational Principle , 1998 .

[5]  Tamás Rapcsák,et al.  New Trends in Mathematical Programming , 1998 .

[6]  K. Fan A generalization of Tychonoff's fixed point theorem , 1961 .

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

[8]  N. D. Yen,et al.  Vector variational inequality as a tool for studying vector optimization problems , 1998 .

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

[10]  S. Itoh,et al.  Variational inequalities and complementarity problems , 1978 .

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

[12]  S. Nadler Multi-valued contraction mappings. , 1969 .

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

[14]  Gue Myung Lee,et al.  Existence of Solutions for Vector Optimization Problems , 1998 .

[15]  G. Lee,et al.  Vector Variational Inequalities in a Hausdorff Topological Vector Space , 2000 .

[16]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[17]  Byung-Soo Lee,et al.  GENERALIZED VECTOR-VALUED VARIATIONAL INEQUALITIES AND FUZZY EXTENSIONS , 1996 .

[18]  Q. H. Ansari,et al.  ON GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES , 1995 .

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

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