Minimax inequality and equilibria with a generalized coercivity

• Autorzy: Chebbi S.
• Języki publikacji: EN

Abstrakty

EN

In the first part of t his paper, we prove a minimax inequality for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part, a result on the existence of maximal element in non-compact domains is obtained and as application, we prove the existence of equilibrium for an abstract economy (or generalized game) with non-compact choice sets.

Słowa kluczowe

EN

coercing family; minimax inequalities; complementarity problems; maximal elements; qualitative games; generalized games; abstract economies

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 1
• Strony: 119--127
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Chebbi S.

• LEGI-Ecole Polytechnique de Tunisie and Faculté des Sciences de Bizerte B.P. 743, 2078 La Marsa, Tunis, Tunisia,

Bibliografia

• [1] Allen, G., Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. Appl. 58 (1977), 1-10.
• [2] Ben-El.Mechaiekh, H., Chebbi, S., Florenzano, M., A generalized KKMF principle, J. Math. Anal. Appl. (in press).
• [3] Ben-EI-Mechaiekh, H., Deguire, P., Granas, A., Points fixes et coincidences pour les applications multivoques (applications de Ky Fan), C. R. Acad. Sci. Paris, ser. I Math. 295 (1982), 257-259.
• [4] Borglin, A., Keiding, H., Existence of equilibrium actions and of equilibrium: A note on the "new" existence theorems, J. Math. Econom. 3 (1976), 313-316.
• [5] Ding, X. P., Tan, K. K., On equilibria of non compact generalized games, J. Math. Anal. Appl. 177 (1993), 226-238.
• [6] Fan, K., Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537.
• [7] Gale, D., Mas-Collel, A., Corrections to an equilibrium existence theorem for a general model without ordered preferences, J. Math. Econom. 6 (1979), 297-298.
• [8] Karamardian, S., Genemlized complementarity problem, J. Optim. Theory Appl. 8 (1971), 161-168.
• [9] Toussaint, S., On the existence of equilibria in economies with infinitely many commodities and without ordered preferences, J. Econom. Theory 33 (1984), 98-115.
• [10] Tulcea, C. I., On the approximation of upper semicontinuous correspondences and the equilibrium of generalized games, J. Math. Anal. Appl. 136 (1988), 267-289.
• [11] Yen, C. L., A minimax inequality and its applications to variational inequalities, Pacific J. Math. 97 (1981), 477-481.