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Generalized minimax theorems for two set-valued mappings

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  • The generalized minimax theorems of two real set-valued mappings, which generalize and improve the corresponding conclusions of D. Kuroiwa (Appl. Math. Lett., 1996, 9: 97-101.) and Li et.al.(J. Optim. Theory Appl., 2000, 106: 183-200; J. Math. Anal. Appl., 2003, 281: 707-723.), and the generalized minimax theorems of two set-valued mappings valued in Fréchet spaces are proved. Some examples are given also to show the results.
    Mathematics Subject Classification: Primary: 49J53; Secondary: 49K35.


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  • [1]

    J. P. Aubin and I. Ekeland, "Applied Nonlinear Analysis," John Wiley and Sons, New York, 1984.


    F. Ferro, A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60 (1989), 19-31.doi: 10.1007/BF00938796.


    K. Fan, Sur un théorème minimax, C. R. Acad. Sci. Paris, 259 (1964), 3925-3928.


    C. W. Ha, Minimax and fixed point theorems, Mathematische Annalen, 248 (1980), 73-77.


    D. Kuroiwa, Convexity for set-valued maps, Appl. Math. Lett., 9 (1996), 97-101.doi: 10.1016/0893-9659(96)00020-1.


    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.


    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.


    D. T. Luc, "Theory of Vector Optimization," in "Lecture Notes in Economics and Mathematical Sesytems" 319, 1988.


    J. W. Nieuwenhuis, Some minimax theorems in vector-valued functions, J. Optim. Theory Appl., 40 (1983), 463-475.doi: 10.1007/BF00933511.


    W. Rudin, "Functional Analysis," McGraw-Hill, Inc., 1973.


    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.


    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.


    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.


    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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