# 臺灣博碩士論文加值系統

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 在這篇論文裡，我們首先證明多值映射或向量值函數的推廣向量鞍點存在定理，然後導出推廣向量極大極小值定理的存在定理。我們也可以建立向量值函數的推廣向量quasi- variational-like不等式問題的存在定理及推廣向量鞍點問題和推廣向量quasi- variational- like不等式問題；兩者間解的關係，由此我們又建立出另一個向量鞍點問題的存在定理。
 In this paper, we first prove some existence theorems of generalized vector saddle point for multivalued map or vector valued function. As a consequence, we establish the existence theoremsof generalized vector minimax theorem. We also establish the existencetheorem of generalized vector quasi-variational-like inequality problem for vector valued function and the relationship between the solutions of the generalized vector saddle point problem and the generalized vectorquasi-variational-like inequality problem for vector valued functions.From which we establish another existence theorem of generalized vector saddle point problems.
 1.Abstract and Introduction ………………… 1 2.Preliminaries ……………………………… 4 3.Generalized vector saddle point……………… 10 4.Generalized vector minimax theorems ……… 17 5.Generalized vector saddle point problem and generalized vector quasi-variational-like inequality problem …………………… 23 References …………………………………… 33
 1.Lai-Jiu Lin, On generalized loose saddle point theorems for set valued maps, Proceeding of Nonlinear Analysis and Convex Analysis, World Scientific, Niigata, Japan, 1999.2.D. T. Luc and C. Vargas, A saddle point theorem for set-valued maps, Nonlinear Anal. Theory, Meth. Appl. , 18 (1992), 1-7.3.T. Tanaka, Generalized quasiconvexities, cone saddle points and minimax theorem for vector-valued functions, J. Math. Anal. Appl., 81, 355-377, (1994).4.T. Tanaka, Minimax theorems of vector-valued functions, In Nonlinear Analysis and Mathematical Economics,(Edited by W. Takahashi),RIMS, Vol. 861, Kyoto University, Kyoto,Japan,(1994).5.T. Tanaka, Existence theorems for cone saddle points of vector-valued functions in infinite dimensional spaces, J. Optim. Theory and Appl. 62, 127-138,(1989).6.T. Tanaka, Two types of minimax theorems for vector-valued functions,J. Optim. Theory and Appl. 68, 321-334, (1991).7.F. Ferro, A minimax theorem for vector-valued functions (I), J. Optim. Theory and Appl. 60,19-31 (1989).8.F. Ferro, A minimax theorem for vector-valued functions (II), J. Optim. Theory and Appl. 68, 35-48 (1991).9.D. S. Shi and C. Ling, Minimax theorems and cone saddle points of uniformly same-order vector-valued functions, J. Optim. Theory Appl. 84, 575-587.10.K. K. Tan, J. Yu and X. Z. Yuan, Existence theorems for saddle points of vector valued maps,J. Optim. Theory and Appl. 89, (1996), 731-747.11.S. Park, Some coincidence theorems on acyclic multifunctions and applications to KKM theory, in " Fixed point theory and applications " (K. K. Tan eds), World Scientific, Singapore, (1992), 248-277.12.D. T. Luc, Theory of Vector Optimization, Lecture Notes in Economics and Mathematical,Systems, Vol. 319, Springer, Berlin, 1989.13.Y. Chiang, O. Chadli and J. C. Yao, On the existence of quasi implicit vector variational inequalities, Journal of Optimization Theory and Applications, 2002(to appear).14.A. Ben-Israel and B. Mond, 'What is invexity' , J. Austral. Math. Soc. 28(1986), 1-9.15.M. A. Hanson, 'On the sufficiency of the Kuhn-Tucker conditions', J. Math. Anal. Appl. 80(1981),545-550.16.L. J. Lin and Z. T. Yu, On generalized vector quasi-equilibrium problems for multimaps, J. Computational and Applied Math. 129,(2001),171-183.17.J. P. Aubin, A. Cellina, Differential Inclusion , Springer, Berlin, (1994).18.Lin, L. J., Generalized Quasi-Equilibrium Problems for Multimaps, Proceeding of International Conferences of Optimizations: Technical and Applications, 1998.19.B. S. Lee, G.M. Lee and S. S. Chang, Generalized vector variational inequalities for multifunctions, Proceedings of workshop on fixed point theory, Annales universitatis Mariae Curie-Sklodowska, Lubin-Polonia Vol. L. I. 2(1997), 193-202.20.Tan, N. X., Quasi-variational inequalities in topological linear locally convex Hausdorff spaces, Mathematische Nachrichten, Vol. 122, pp.231-245, 1985.21.W. S. Massey, Singular Homology Theory , Springer Verlag, New York, 1980.22.K. Fan, Fixed point and minimax theorems in locally convex topological linear spaces , Pro. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126.23.S. S. Chang, G. X. Z. Yuan, G.H. Lee and Xiao Lan Zhang, Saddle Points and Minimax Theorems for Vector-Valued Multifunctions on H-spaces, Applied Mathematics Letters, Vol. 11, No.3, pp. 101-107 (1998).24.K. R. Kazmi and S. Khan, Existence of solutions for a vector saddle point problem,Bull. Austral. Math. Soc. Vol. 61(2000) 201-206.
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 1 G-KKM族在廣義凸空間上的同值點定理 2 鞍點不等式

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