臺灣博碩士論文加值系統

在這一篇論文裡，我們首先建立史坦巴西亞型式的平衡點存在定理，然後利用最大值定理去建立明梯型式的平衡點存在結果，並且利用一個平衡點定理建立另一種沒有限制條件的明梯型式的平衡點存在定理。

In this paper, we first estabilish the existence results of the Stampacchia type equilibrium problems. Then we apply the maximal element theorem to establish the exisence theorems of Minty type equilibrium problems. We also establish another existing results of the Minty type without constrainted correspondence by an equilibrium theorem.

1.Abstract and Introduction……………1
2.Preliminaries……………………………4
3.Stampacchia type Equilibrium Problems
…………………………………………6
4.Minty type Equilibrium Problems
…………………………………………15
Reference……………………………………26

[1] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, New York, (1980).
[2] F. Gianessi, On Minty variational principle, In F. Gianessi, S. Komlo'si, and T. Rapcsa'k, editors, New Trends in Mathematical Programming, Kluwer Academic Publishers, Dordrecht, (1998).
[3] G. Kassay and J. Kolumb'an, Variational inequalities given by semi-pseudomonotone mappings, Nonlinear Analysis Forum, 5 (2000), 35-50.
[4] G. Kassay, T. Kolumb'an and Zs. Pa'les , Factorization of Minty and Stampacchia variational inequality systems, to appear in European Journal of Operations Research.
[5] H. Kneser, Sur une th'eoreme fondamental de la th'eorie des jeux, Comptes Rendus de L'Acad. des Sci. de Paris 243 (1952), 2418-2420.
[6] J. P. Aubin and A. Cellina, Differential inclusions, Springer-Verlag, Berlin, Heidberg, New York, (1994).
[7] L. J. Lin and Z. Y. Yu, On some equilibrium problems for multimaps, J. Comput. Appl. Math. 129 (2001), 171-183.
[8] L. J. Lin, Z. Y. Yu and G. Kassay, Existence of equilibria for multivalued mappings and its applications to vectorial equilibria, J. of Optim. Theory and Appli. 114(1) (2002), 189-208.
[9] P. Deguire, K. K. Tan, G. X. Z. Tuan, The study of maximal elements, fixed points for Ls-majorized mappings and their applications to minimax and variational inequalities in product spaces, Nonlinear Analysis 37 (1999), 933-951.
[10] Q. H. Ansari and J. C. Yao, A existence result for the generalized vector equilibrium problem , Appl. Math. Lett., 12(8) (1999), 53-56.
[11] S. Komlo'si, On the Stampacchia and Minty variational inequalities, In G Giorgi and F. A. Rossi, editors, Generalized Convexity and Optimization for Economic and Financial Decisions. Pitagora Editrice, Bologna, (1999).
[12] Y. C. Yao, Multi-valued variational inequalities with K-pseudomonotone operators, Journal of Optimization Theory and Applications, 883 (1999), 391-403.
[13] Y. Q. Chen, On semi-monotone operator theory and applications, Journal of Math. Anal. and Appl. 231 (1999), 177-192.