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Bibliography

1
G. Allen, Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. Appl. 58 (1977), 1-10.

2
Q. H. Ansari and J.-C. Yao, An Existence Result for the Generalized Vector Equilibrium Problem, Appl. Math. Let. 12 (1999), 53-56.

3
J .P. Aubin, Optima and Equilibria, An introduction to nonlinear analysis, Springer-Verlag, Berlin-Heidelberg, 1993.

4
H. Ben-El-Mechaiekh, P. Deguire, and A. Granas, Une alternative non linéaire en analyse convexe at applications, C. R. Acad. Sci. Paris Série I 295 (1982), 257-259.

5
M. Bianchi, N. Hadjisavvas and S. Schaible, Vector Equilibrium Problems with Generalized Monotone Bifunctions, J. Optim. Theo. Appl. 92 No 3 (1997), 527-542.

6
M. Bianchi and S. Schaible, Generalized Monotone Bifunctions and Equilibrium Problems, J. Optim. Theo. Appl. 90 (1996), 31-43.

7
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Stud. 63 (1994), 123-145.

8
H. Brézis, L. Nirenberg and G. Stampacchia, A remark on Ky Fan's minimax principle, Boll. Unio. Mate. Ital. 4 (1972), 293-300.

9
O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities, J. Optim. Theo. Appl. 105 (2000), no. 2, 299-323.

10
S. S. Chang and Y. Zhang, Generalized KKM theorem and variational inequalities, J. Math. Anal. Appl. 159 (1991), 208-223.

11
G. Y. Chen, Existence of Solutions for a Vector Variational Inequality: An Extension of Hartman-Stampacchia Theorem, J. Optim. Theo. Appl. 74 (1992), 445-456.

12
G. Y. Chen and G. M. Cheng, Vector Variational Inequality and Vector Optimization, Lecture Notes in Econom. Math. Syst., Vol. 285, 408-416, Springer-Verlag, Berlin, 1987.

13
G. Y. Chen and B. D. Craven, Approximate Dual and Approximate Vector Variational Inequality for Multiobjective Optimization, J. Aust. Math. Soc. Serie A (1989), 418-423.

14
G. Y. Chen, C. J. Goh and X. Q. Yang, Vector Network Equilibrium Problems and Nonlinear Scalarization Methods, ZOR - Math. Mod. Oper. Res. 49 (1999), 239-253.

15
S. Dafermos and A. Nagurney, Oligopolistic and competitive behavior of Spatially Separated Markets, Regi. Sci. Urban Econ. 17 (1987), 245-254.

16
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amestardam, 1976.

17
G. Evans, Overview of Techniques for Solving Multiobjective Mathematical Programs, Mana. Sci. 30 No. 11 (1984), 1268-1282.

18
Ky Fan, A generalization of Tychonoff's fixed point theorem, Math. Annal. 142 (1961), 305-310.

19
Ky Fan, A minimax inequality and application, in ``Inequalities'' (Edited by O. Shisha) Vol. 3, 103-113, Academic Press, New York, 1972.

20
K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537.

21
F. Ferro, Minimax type theorems for n-valued functions, Anna. Mate. Pura Appl. 32 (1982), 113-130.

22
M. Florian and M. Los, A New Look at Static Spatial Price Equilibrium, Regi. Sci. Urban Econ. 12 (1982), 579-597.

23
P. Georgiev and T. Tanaka, Fan's Inequality for Set-Valued Maps, Nonlinear Anal. 47 (2001), 607-618.

24
F. Giannessi, Theorems of alternative quadratic programs and complementarity problems, in Variational Inequalities and Complementarity Problems (Eds. Cottle, Giannessi and Lions), 151-186, John Wiley and Sons, Chicherster, 1980.

25
F. Giannessi (Ed.), Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999.

26
A. Goepfert, H. Riahi, C. Tammer and C. Zalinescu, Variational methods in Partially Ordered Spaces, in preparation.

27
N. Hadjisavvas and S. Schaible, From scalar to vector equilibrium problems in the quasimonotone case, J. Optim. Theo. Appl. 96 No 2 (1998), 297-309.

28
P. T. Harker and J.-S. Pang, Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications, Math. Prog., 48 (1990), 161-220.

29
B. Hartman and G. Stampacchia, On Some Nonlinear Elliptic Differential Functional Equations, Acta Math. 115 (1966), 271-310.

30
C. Horvath, Points fixes et coïncidences pour les applications multivoques sans convexité, C. R. Acad. Sci. Paris Série I 295 (1983), 403-406.

31
C. Horvath, Some results on multivalued mappings and inequalities without convexity, in Nonlinear and Convex Analysis--Proceedings in Honor of Ky Fan (Eds. B.-L. Lin and S. Simons), pp 99-106, Dekker, New York, 1987.

32
J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces, Peter Lang, Frankfurt, 1986.

33
J. Jahn, Set-Valued Optimization: A Survey, Preprints des Institus für Angewandte Mathematik der Universität Erlangen-Nürenberg No. 264, 2000.

34
E. M. Kalmoun, On Ky Fan's Minimax Inequalities, Mixed Equilibrium Problems and Hemivariational Inequalities, JIPAM J. Ineq. Pure Appl. Math., 2 Issue 1 (2001), Article 12.

35
E. M. Kalmoun and H. Riahi, Topological KKM Theorems and Generalized Vector Equilibria on G-Convex Spaces with Applications, Proc. Amer. Math. Soc., 129 (2001), 1335-1348.

36
D. Kinderlehrer and G. Stampacchia, An Introduction to variational inequalities and their applications, Academic Press, New York, 1980.

37
B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunktsatsez für n-dimensionale simplexe, Fund. Math. XIV (1929), 132-137.

38
I. V. Konnov and J. C. Yao, On The Generalized Vector Variational Inequality Problem, J. Math. Anal. Appl. 206 (1997), 42-58.

39
I. V. Konnov and J. C. Yao, Existence of Solutions for Generalized Vector Equilibrium Problems, J. Math. Anal. Appl. 233 (1999), 328-335.

40
M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201.

41
L.-J. Lin and Z.-T. Yu, Fixed-point theorems and equilibrium problems, Nonlinear Anal. 43 (2001) 987-999.

42
D. The Luc, Theory of Vector Optimization, Springer-Verlag, Berlin, 1989.

43
A. Nagurney, Network Economics: A Variational Inequality Approach (Revised second edition), Kluwer Academic Publishers, Dordrecht, 1999.

44
A. Nagurney, J. Dong and M. Hughes, Formulation and Computation of General Financial Equilibrium, Optim. 26 (1992), 339-354.

45
A. Nagurney and L. Zhao, Variational Inequalities and Networks in the Formulation and Computation of the Market Equilibria and Disequilibria: The Case of Direct Demand Functions, Trans. Sci. 27 (1993), 4-15.

46
Z. Naniewicz and P. D. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker, Inc. New York, 1995.

47
W. Oettli, A remark on vector-valued equilibria and generalized monotonicity, Acta Math. Viet. 22 (1997), 213-212.

48
W. Oettli and D. Schläger, Generalized vectorial equilibria and generalized monotonicity, in Functional Analysis with Current Applications, (Edited by M. Brokate and A. H. Siddiki), Longman, London, 1997.

49
W. Oettli and D. Schläger, Existence of equilibria for monotone multivalued mappings, Math. Meth. Oper. Res. 48 (1998), 219-228.

50
P. D. Panagiotopoulos, Non-Convex Superpotentiels in the Sense of F. H. Clarke and Applications, Mech. Res. Comm. 8 (1981), 335-340.

51
S. Park and H. Kim, Admissible Classes of Multifunctions on Generalized Convex Spaces, Proc. Coll. Natur. Sci. Seoul National University 18 (1993), 1-21.

52
M.-H. Shih and K.-K. Tan, A further generalization of Ky Fan's minimax inequality and its applications, Studia Math.78 (1984), 279-287.

53
A. H. Siddiqi, Q. H. Ansari and A. Khaliq, On Vector Variational Inequalities, J. Optim. Theo. Appl. 84 (1995), 171-180.

54
S. Simons, Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, Proc. Symp. Pure Math. 45 (1986), 377-392.

55
A. Takayama, Mathematical Economics, The Dryden Press, Hinsdale IL., 1974.

56
K.-K Tan, J. Yu and X.-Z. Yuan, Some new minimax inequalities and applications to existence of equilibria in H-spaces, Nonlinear Anal. 24 (1995), 1457-1470.

57
T. Tanaka, Existence Theorems for Cone Saddle Points of Vector-Valued Functions in Infinite Dimensional Spaces, J. Optim. Theo. Appl. 62 (1989), 127-138.

58
T. Tanaka, Generalized Quasiconvexities, Cone Saddle Points, and Minimax Theorem for Vector-Valued Functions, J. Optim. Theo. Appl. 81 No 2 (1994), 355-377.

59
T. Tanaka, Existence Theorems for Cone Saddle Points and Vector-Valued Minimax Theorems, in Lecture Notes in Economics and Mathematical Systems (Edited by R. Caballero, F. Ruiz and R.E. Steuer), Vol.455, 210-218, Springer, 1997.

60
T. Tanaka, Vector-Valued Minimax Theorems in Multicriteria Games, in ``New Frontiers of Decision Making for the Information Technology Era,'' (Edited by Yong Shi and Milan Zeleny), 75-99, World Scientific, 2000.

61
E. Tarafdar and X.-Z Yuan, Generalized variational inequalities and its applications, Nonlinear Anal. Theo. Meth. Appl. 30 (1997), 4171-4181.

62
G. Tian, Generalizations of the FKKM theorem and the Ky Fan minimax inequality with applications to maximal elements, price equilibrium, and complementarity, J. Math. Anal. Appl. 170 (1992), 457-471.

63
G. Wanka, On duality in the vectorial control-approximation problem, ZOR-Meth. Mod. Oper. Res. 35 (1991), 309-320.

64
K. C. Wu, Multi-Criterion Preliminary Design of a Tetrahederal Truss Platform, presented at the 36th AIAA/ASME/ASCE/AHE/ASC Structures, Structural Dynamics, and Materials Conference, New Orleans LA, 10-13 April, AIAA 95-1327, 1995.

65
X. Q. Yang, vector variational inequality and its duality, Nonlinear Anal. Theo. Meth. Appl. 21 No 11 (1993), 869-877.

66
C. L. Yen, A minimax inequality and its applications to variational inequalities, Pacific J. Math. 97 (1981), 477-481.

67
X. Z. Yuan, The study of minimax inequalities and applications to economies and variational inequalities, Memo. Amer. Math. Soc. 132 (1998), N. 625.

68
L. Zhao and S. Dafermos, General Economic Equilibrium and Variational Inequalities, Oper. Res. Let. 10 (11), 369-376.

69
J. X. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities, J. Math. Anal. Appl. 132 (1988), 213-225.



El Mostafa Kalmoun
Visiting Professor of the Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan.


El Mostafa Kalmoun 2002-12-20