研究生: |
羅崑宗 |
---|---|
論文名稱: |
在可允許凸子集上的同值點定理 |
指導教授: | 張東輝 |
口試委員: | |
學位類別: |
碩士 Master |
系所名稱: |
|
論文出版年: | 2005 |
畢業學年度: | 94 |
語文別: | 中文 |
論文頁數: | 19 |
中文關鍵詞: | 凸空間 、同值點定理 、大中取小不等式 、(特殊符號無法顯現請參閱PDF檔 |
外文關鍵詞: | convex space, coincidence theorem, minimax inequalities, (特殊符號無法顯現請參閱PDF檔 |
相關次數: | 點閱:2 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
摘 要
設X 是一個拓樸向量空間的可允許的凸子集,Y 是一個拓樸空間,T屬於s-KKM ,F是一個從Y 映到X 的 -函數。在某些假設條件之下,我們證得T與F的一些同值點定理。我們也利用上面結果證明兩個 -函數的一些同值點定理和大中取小不等式的存在性定理
Abstract
Let X be an admissible convex subset of a topological vector space, let Y be a topological space, let , and let be a . In this paper, we establish a coincidence theorem of T and F under some assumptions. By using the above theorem, we also establish a coincidence theorem for two and get the existence theorem concerning minimax inequalities.
(特殊符號無法顯現請參閱PDF檔)
REFERENCES
[1] Q. H. Ansari, A. Idzik, and J. C. Yao, Coincidence and fixed point theorems with applications, Topol. Methods Nonlinear Anal. 15(2000), 191-202.
[2] H. Ben-El-Mechaiekh, P. Deguire, and A. Granas, Points fixes et coincidences pour les functions multivoques II, C. R. Acad. Sci. Paris Ser. I 295(1982), 381-388.
[3] K. C. Border, Fixed point theorems with applications to economics and game theory, Cambridge University Press, 1989.
[4] S. S. Chang and Y. Zhang, Generalized KKM theorem and variational inequalities, J. Math. Anal. Appl. 159(1991), 208-233.
[5] T. H. Chang and C. L. Yen, Generalized KKM property and fixed point theorems, J. Math. Anal. Appl. 203(1996), 224-235.
[6] T. H. Chang, Y. Y. Huang, J. C. Jeng, K. W. Kuo, On S-KKM property and related topics, J. Math. Anal. Appl. 229(1999), 212 –227.
[7] T. H. Chang, Y. Y. Huang, J. C. Jeng, Fixed-point theorems for multifunctions in S-KKM class, Nonl. Anal. 44(2001), 1007-1017.
[8] P. Deguire and M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5(1995), 261-269.
[9] P. Deguire, K. K. Tan, and G. X. Z. Yuan, The study of maximal elements, fixed point for -majorized mappings and their applications to minimax and variational inequalities in product topological spaces, Nonlinear Anal. 37(1999), 933-951.
[10] X. P. Ding, Best approximation and coincidence theorems, J. Sichuan Normal
Univ. Nat. Sci. 18(1995), 21-29.
[11] X. P. Ding, Coincidence theorems in topological spaces and their applications, applied. Math. Lett. 12(1999), 99-105.
[12] X. P. Ding, Existence of solutions for quasi-equilibrium problems in noncompact topological spaces, Comput. Math. Appl. 39(2000), 13-21.
[13] X. P. Ding and J. Y. Park, Fixed points and generalized vector equilibrium problems in generalized convex spaces, Indian J. Pure Appl. Math. 34(6)(2003), 973-990.
[14] K. Fan, A generalization of Tychonoff’s fixed point theorem, Math. Ann. 142(1961), 305-310.
[15] K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266(1984), 519-537.
[16] A. Granas and F. C. Liu, Coincidence for set valued maps and inequalities, J.
Math. Anal. Appl. 165(1986), 119-148.
[17] B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunksatzes
fur n-dimensionale simplexe, Fund. Math. 14(1929),132-137.
[18] V. Klee, Leray-Schauder theory without local convexity, Math. Ann. 141(1960), 286 – 297.
[19] F. J. Liu, On a form of KKM principle and supinfsup inequalities of von Neumann and Ky Fan type, J. Math. Anal. Appl. 155(1991), 420-436.
[20] L. J. Lin and H. I. Chen, Coincidence theorems for family of multimaps and their applications to equilibrium problems, J. Abstr. Anal. 5(2003), 295-305.
[21] L. J. Lin, System of coincidence theorems with applications, J. Math. Anal. Appl. 285(2003), 408-418.
[22] M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97(1983), 151-201.
[23] Y. J. Lin and G. Tina, Minimax inequalities equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem, Appl. Math. Optim. 28(1993), 173-179.
[24] J. von Neumann, Uber ein okonomsiches Gleichungssystem und eine
Verallgemeinering des Browerschen Fixpunktsatzes, Ergeb. Math. Kolloq. 8(1937), 73-83.
[25] M. Nagumo, Degree of mappings in convex linear topological spaces, Amer. J.
Math. 73 (1951).
[26] S. Park, Foundations of the KKM theory via coincidences of composites of upper semi-continuous maps, J. Korean Math. Soc. 31(1994), 164-176.
[27] N. Shioji, A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, Proc. Amer. Math. Soc. 111(1991), 187-195.
[28] G. Q. Tina, Generalized KKM theorem, minimax inequalities and their applications, J. Optim. Theory Appl. 83(1994), 375-389.
[29] G. Tina and J. Zhou, Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization, J. Math. Econom. 24(1995), 281-303.
[30] Z. T. Yu and L. J. Lin, Continuous selection and fixed point theorems, Nonlinear Anal. 52(2003), 445-453.