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研究生:江雅雯
研究生(外文):Ya-Wen Chiang
論文名稱:廣義向量變分不等式
論文名稱(外文):A Generalized Vector Variational Inequality for Set-Valued Maps
指導教授:張秀瑜張秀瑜引用關係
指導教授(外文):Shiow-Yu Chang
學位類別:碩士
校院名稱:東吳大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:16
中文關鍵詞:向量變分不等式KKM定理
外文關鍵詞:vector variational inequalityKKM theorem
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摘要(Abstract)
在這篇論文中,我們考慮一個廣義向量變分不等式,且用多值函數的一些條件來作為延伸。我們用KKM定理做出廣義向量變分不等式是有解的存在。

Abstract. In this paper, we study a generalized vector variational inequality, and we extend it for set-valued maps with some kinds of conditions. We establish the extence of solution for generalized vector variational inequality by using KKM THEOREM.

目 錄 (Table of Content)
章 節 標 題 頁 次
致謝(Acknowledgement) i
目錄(Table of Content) ii
摘要(Abstract) iii
第一章 引言
(Introduction)…………………………1
第二章 預備
(Preliminaries)…………………………3
第三章 存在性定理
(Existence Theorem)……………………5
附 註(Reference)………………………15

References
[1] F. Giannessi, Theorem of the Alternative, Quadratic Programs, and Complementarity Programs, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, Wiley, New York, pp. 151-186, 1980.
[2] G. Y. Chen, and G. M. Cheng, Vector Variational Inequalities and Vector Optimization, In Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Heidelberg, Germany, Vol. 258, 1987.
[3] G. Y. Chen, and B. D. Craven, Approximate Dual and Approximate Vector Variational Inequality for Multiobjective Optimization, J. Austral. Math. soc. (Series A) 47, 418-423, 1989.
[4] G. Y. Chen, and B. D. Craven, A vector variational inequality and optimization over an efficient set, Zor-Meth. and Models. of Operatons Research 34, 13-27, 1990.
[5] G. Y. Chen and X. Q. Yang, The Vector Complementarity Problem and Its Equivalence With The Weak Minimal Element in Ordered Sets, J. Math. Anal. Appl. 153, 136-158, 1990.
[6] G. Y. Chen, Existence of Solutions for a vector variational inequality: An extension of Hartman-Stampacchia theorem, J. Optim. Th. Appl. 74 (3), 445-456, 1992.
[7] G. Y. Chen, and S.J. Li, Existence of Solutions for a generalized vector quasivariational inequalies, J. Optim. Th. Appl. 90 (3), 321-334, 1996.
[8] G. M. Lee, D.S. Kim, B.S. Lee and S.J. Cho, Generalized vector variational inequality and fuzzy extension, Appl. Math. Lett. 6 (2), 47-51, 1993.
[9] G. M. Lee, B.S. Lee and S.-S. Chang, On vector quasivariational inequalities, J. Math. Anal. Appl. 203, 626-683, 1996.
[10] G. M. Lee, D.S. Kim, B.S. Lee, Generalized vector variational inequality, Appl. Math. Lett. 9 (1), 39-42, 1996.
[11] S. J. YU, and J. C. YAO, On vector variational inequalities, J. Optim. Th. Appl. 89 (3), 749-769, 1996.
[12] G. M. Lee, D.S. Kim, B.S. Lee, G. Y. Chen, Generalized vector variational inequality and it's duality for set-valued maps, Appl. Math. Lett. 11 (4), 21-26, 1998.
[13] George Xian-Zhi Yuan, KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker, Inc., New York, 1999.
[14] Kim C. Border, Fixed Point Theorems with Application to Economics and Game Theory, New York: Cambridge University Press, 1985.

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