Existence theorems for vector variational inequalities

Bulletin of the Australian Mathematical Society

Volumn 54, Issue 3, 1996, Pages 473-481

  Daniilidis, Aris ^a   Hadjisavvas, Nicolas ^a  

^a UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001159469     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0004972700021882     Document Type: Article

References (17)

1. J.M. Borwein and A.S. Lewis, 'Partially finite convex programming, Part I: Quasi relative interiors and duality theory', Math. Programming 57 (1992), 15-48.
2. G.-Y. Chen, 'Existence of solutions for a vector variational inequality: An extension of the Hartman-Stampacchia theorem', J. Optim Theory Appl. 74 (1992), 445-456.
3. G.-Y. Chen and X.-Q. Yang, 'The vector complementarity problem and its equivalences with the weak minimal element in ordered spaces', J. Math. Anal. Appl. 153 (1990), 136-158.
4. G.-Y. Chen and B.D. Craven, 'A vector variational inequality and optimization over an efficient set', Z. Oper. Res. 3 (1990), 1-12.
5. J. Diestel and J.J. Uhl, Vector measures (American Mathematical Society, Providence, R.I., 1970).
6. N. Dunford and J.T. Schwartz, Linear operators Part I: General theory (Wiley, New York, 1988).
7. K. Fan, 'A generalization of Tychonov's fixed-point theorem', Math. Annal. 142 (1961), 305-310.
8. F. Giannessi, 'Theorems of alternative, quadratic programms and complementarity problems', in Variational inequalities and complementarity problems, (R.W. Cottle, F. Giannessi and J.L. Lions, Editors) (Wiley, New York, 1980), pp. 151-186.
9. N. Hadjisavvas, D. Kravvaritis, G. Pantelidis and I. Polyrakis, 'Nonlinear monotone operators with values in L(X, Y)', J. Math. Anal. Appl. 140 (1989), 83-94.
10. N. Hadjisavvas and S. Schaible, 'Quasimonotone variational inequalities in Banach spaces', J. Optim. Theory Appl. 90 (1996), 95-111.
11. G. Jameson, Ordered linear spaces, Lecture Notes in Mathematics 141 (Springer-Verlag, Berlin, Heidelberg, New York, 1970).
12. S. Karamardian and S. Schaible, 'Seven kinds of monotone maps', J. Optim. Theory Appl. 66 (1990), 37-46.
13. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications (Academic Press, New York, 1980).
14. G.M. Lee, D.S. Kim, B.S Lee and S.J. Cho, 'Generalized vector variational inequalities and fuzzy extensions', Appl. Math. Lett. 6 (1993), 47-51.
15. D.T. Luc, 'Characterisations of quasiconvex functions', Bull. Austral. Math. Soc. 48 (1993), 393-406.
16. M.H. Shi and K.K. Tan, 'Browder-Stampacchia variational inequalities for multivalued monotone operators', J. Math. Anal. Appl. 134 (1988), 431-440.
17. X.Q. Yang, 'Vector complementarity and minimal element problems', J. Optim. Theory Appl. 77 (1993), 483-495.