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Generalized minimax theorems for two set-valued mappings
1. | College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China |
2. | College of Applied Sciences, Beijing University of Technology, Beijing 100124, China, China |
References:
[1] |
J. P. Aubin and I. Ekeland, "Applied Nonlinear Analysis," John Wiley and Sons, New York, 1984. |
[2] |
F. Ferro, A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60 (1989), 19-31.
doi: 10.1007/BF00938796. |
[3] |
K. Fan, Sur un théorème minimax, C. R. Acad. Sci. Paris, 259 (1964), 3925-3928. |
[4] |
C. W. Ha, Minimax and fixed point theorems, Mathematische Annalen, 248 (1980), 73-77. |
[5] |
D. Kuroiwa, Convexity for set-valued maps, Appl. Math. Lett., 9 (1996), 97-101.
doi: 10.1016/0893-9659(96)00020-1. |
[6] |
S. J. Li, G. Y. Chen and G. M. Lee, Minimax theorems for set-valued mappings, J. Optim. Theory Appl., 106 (2000), 183-199.
doi: 10.1023/A:1004667309814. |
[7] |
S. J. Li, G. Y. Chen, K. L. Teo and X. Q. Yang, Generalized minimax inequalities for set-valued mappings, J. Math. Anal. Appl., 281 (2003), 707-723.
doi: 10.1016/S0022-247X(03)00197-5. |
[8] |
D. T. Luc, "Theory of Vector Optimization," in "Lecture Notes in Economics and Mathematical Sesytems" 319, 1988. |
[9] |
J. W. Nieuwenhuis, Some minimax theorems in vector-valued functions, J. Optim. Theory Appl., 40 (1983), 463-475.
doi: 10.1007/BF00933511. |
[10] | |
[11] |
K. K. Tan, J. Yu and X. Z. Yuan, Existence theorems for saddle points of vector-valued maps, J. Optim. Theory Appl., 89 (1996), 731-747.
doi: 10.1007/BF02275357. |
[12] |
T. Tanaka, Generalied quasiconvexities, cone saddle points and minimax theorems for vector-valued functions, J. Optim. Theory Appl., 81 (1994), 355-377.
doi: 10.1007/BF02191669. |
[13] |
Q. B. Zhang and C. Z. Cheng, Some fixed-point theorems and minimax inequalities in FC-space, J. Math. Anal. Appl., 328 (2007), 1369-1377.
doi: 10.1016/j.jmaa.2006.06.027. |
[14] |
Q. B. Zhang, M. J. Liu and C. Z. Cheng, Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces, Nonlinear Anal., 71 (2009), 212-218.
doi: 10.1016/j.na.2008.10.040. |
show all references
References:
[1] |
J. P. Aubin and I. Ekeland, "Applied Nonlinear Analysis," John Wiley and Sons, New York, 1984. |
[2] |
F. Ferro, A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60 (1989), 19-31.
doi: 10.1007/BF00938796. |
[3] |
K. Fan, Sur un théorème minimax, C. R. Acad. Sci. Paris, 259 (1964), 3925-3928. |
[4] |
C. W. Ha, Minimax and fixed point theorems, Mathematische Annalen, 248 (1980), 73-77. |
[5] |
D. Kuroiwa, Convexity for set-valued maps, Appl. Math. Lett., 9 (1996), 97-101.
doi: 10.1016/0893-9659(96)00020-1. |
[6] |
S. J. Li, G. Y. Chen and G. M. Lee, Minimax theorems for set-valued mappings, J. Optim. Theory Appl., 106 (2000), 183-199.
doi: 10.1023/A:1004667309814. |
[7] |
S. J. Li, G. Y. Chen, K. L. Teo and X. Q. Yang, Generalized minimax inequalities for set-valued mappings, J. Math. Anal. Appl., 281 (2003), 707-723.
doi: 10.1016/S0022-247X(03)00197-5. |
[8] |
D. T. Luc, "Theory of Vector Optimization," in "Lecture Notes in Economics and Mathematical Sesytems" 319, 1988. |
[9] |
J. W. Nieuwenhuis, Some minimax theorems in vector-valued functions, J. Optim. Theory Appl., 40 (1983), 463-475.
doi: 10.1007/BF00933511. |
[10] | |
[11] |
K. K. Tan, J. Yu and X. Z. Yuan, Existence theorems for saddle points of vector-valued maps, J. Optim. Theory Appl., 89 (1996), 731-747.
doi: 10.1007/BF02275357. |
[12] |
T. Tanaka, Generalied quasiconvexities, cone saddle points and minimax theorems for vector-valued functions, J. Optim. Theory Appl., 81 (1994), 355-377.
doi: 10.1007/BF02191669. |
[13] |
Q. B. Zhang and C. Z. Cheng, Some fixed-point theorems and minimax inequalities in FC-space, J. Math. Anal. Appl., 328 (2007), 1369-1377.
doi: 10.1016/j.jmaa.2006.06.027. |
[14] |
Q. B. Zhang, M. J. Liu and C. Z. Cheng, Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces, Nonlinear Anal., 71 (2009), 212-218.
doi: 10.1016/j.na.2008.10.040. |
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