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研究生:黃裕仁
研究生(外文):Huang, Yu Jen
論文名稱:向量擬平衡問題、向量擬變分包含問題及其在共同固定點定理和最優化問題之應用
論文名稱(外文):Vector Quasi-Equilibrium Problems and Vector Quasi-Variational Inclusion Problems With Applications to Common Fixed Point Theorems and Optimization Problems
指導教授:林來居林來居引用關係
指導教授(外文):Lin, Lai Jiu
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:80
中文關鍵詞:最大擬單調平衡問題上半連續(下半連續)變分包含問題雙重最優化問題平衡限制條件下數學規劃共同固定點
外文關鍵詞:maximal pseudomonotoneequilibrium problemgeneralized u-hemicontinuous (l-hemicontinuous)upper (lower) semicontinuous multivalued mapvariational inclusion problembilevel problemmathematical program with equilibriumcommon fixed point
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中文摘要(I)

在這一篇論文裡,我們首先建立廣義向量擬平衡問題的存在定理,由這問題的存在結果,我們應用到多值映射的加權混和型向量變分不等式問題的存在定理、兩個多值映射的共同固定點定理和平衡限制條件下的 mathematical program 的存在性定理。

中文摘要(II)

在這一篇論文裡,我們建立了系統向量擬變分包含問題的存在定理和系統向量變分包含限制條件下mathematical program的存在定理。由這些問題的存在結果,我們考慮了 bilevel 問題、系統平衡限制條件下 mathematical program 以及兩群多值映射的共同固定點定理。由共同固定點結果的特殊情況,我們考慮了一群 l.s.c. 或nonexpansive 或 k-contractive 多值映射的固定點定理。最後,我們將結果應用到建立系統 Minty 型態和 Stampacchia型態廣義隱變分不等式問題的存在定理。
Abstract(I)

In this paper, we first establish the existence theorems of generalized vector quasi-equilibrium problems. From the above results, we establish the existence theorems of weighted mixed vector variational-like inequality problems for multivalued maps, common fixed point theorems for two multivalued maps and mathematical program with equilibrium constraint as applications.

Abstract(II)

In this paper, we establish the existence theorems of system of vector quasi-variational inclusion problems and the existence theorems of mathematical program with system of variational inclusion constraints. From above results, we study the bilevel problem and mathematical program with system of equilibrium constraints, and we also consider common fixed point theorems for two families of multivalued maps. For the special case, we study the fixed point theorems for a family of lower semicontinuous or nonexpansive or k-contractive multivalued maps. We also study the existence theorems of system of Minty type generalized implicit quasi-variational inequality problems (SMGIQVIP) and system of Stampacchia type generalized implicit quasi-variational inequality problems (SSGQVIP) as applications.
Contents
(I)Generalized Vector Quasi-Equilibrium Problems With Applications to Common Fixed point Theorems and Optimization Problems

1.Introduction............................................1
2.Preliminaries...........................................4
3.The existence theorems of maximal pseudomonotonicity....9
4.The existence theorems of generalized vector quasi-equilibrium problems.....................................13
5.Applications to weighted mixed vector variational-like inequality problems......................................22
6.Applications to common fixed point theorems............31
7.Applications to mathematical program with equilibrium constraint...............................................35
References...............................................41

(II)System of Vector Quasi-Variational Inclusion Problems With Applications to Common Fixed Point Theorems and Optimization problems

1.Introduction..........................................44
2.Preliminaries.........................................48
3.The existence theorems of system vector quasi-variational inclusion problems and mathematical program with system of variational inclusion constraint........................52
4.Applications to common fixed point theorems...........67
5.Applications to system of Minty type and Stampacchia type generalized implicit quasi-variational inequality problems................................................74
References..............................................79
Reference(I)

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[9.] P. Deguire, K. K. Tan and G. X. Z. Yuan, the study of
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[10.] J. Y. Fu and A. H. Wan, Generalized vector equilibria
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Existence results for Stampachia and Minty type implicit
variational inequalities with multivalued maps, Nonlinear Anal., 61(2005), 1-19.

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generalized semi-infinite programming. J. Global Optimization, (2005) (to appear).

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Reference(II)

[1.] Aubin J. P. and Cellina A., (1994), Differential
inclusions, Springer Verlag , Berlin, Heidelberg, Germany.

[2.] Ansari Q. H. and Yao J. C., (1999), An existence result
for the generalized vector equilibrium problems, Applied
Mathematics letters, 12, 53-56.

[3.] Aussel D. and Hadjisavvas N., (2004), On Quasimonotone
Variational Inequalities, Journal of Optimization Theory and
Applications, 121, 445-450.

[4.] Deguire P., Tan K. K. and Yuan G. X. Z., (1999), the
study of maximal elements, fixed point for Ls-majorized mappings and the quasi-variational inequalities in product spaces, Nonlinear Analysis, 37, 933-951.

[5.] Konnov I. V. and Yao J. C., (1999), Existence solutions
for generalized vector equilibrium problems, Journal of
Mathematical Analysis and Applications, 223, 328-335.

[6.] Luc D. T., (1989), Theory of Vector Optimization,
Lecture Notes in Economic and Mathematical, system, Vol 319.
Springer, Berlin,.

[7.] Luc D. T. and Tan N. X., (2004), Existence conditions
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[8.] Lin L. J., (2005), System of generalized vector
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theorems for a family of nonexpansive multivalued mapping, Journal of Global Optimization, (to appear).

[9.] Lin L. J., (2006), System of vector equilibrium with
applications to fixed point theorems for family of $k$-contractive multivalued map, Taiwanese Journal of Mathematics, (to appear).

[10.] Lin L. J., Mathematical programs with equilibrium
constraints: the structure of the feasible set and the existence of feasible point, (preprint).

[11.] Lin L. J., Yang M. F., Ansari Q. H. and Kassay G.,
(2005) Existence results for Stampachia and Minty type implicit variational inequalities with multivalued maps, Nonlinear Analysis, 61, 1-19.

[12.] Minh N. B. and Tan N. X., (2005), On the existence of
solutions of quasi-variational inclusion problems of Stampacchia type, Advance in Nonlinear Variational Inequalities, 8, 1-16.

[13.] Tan N. X., (1985), Quasi-variational inequalities in
topological linear locally convex Hausdorff spaces, Mathematicsche Nachrichen, 122, 231-245.

[14.] Tan N. X., (2004), On the existence of solution of
quasi-variational inclusion problems, Journal of Optimization Theory and Applications, 123, 619-638.

[15.] Takahashi W., (2000), Nonlinear functional analysis ,
Yokohama Publishers, Yokohama.

[16.] Yannelis N. C. and Prabhakar N. D., (1983), Existence
of maximal element and equilibria in linear topological space, Journal of Mathematical Economics, 125, 233-245.
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