G-凸空间中的择一原理和极大极小不等式

M·巴拉奇

G-凸空间中的择一原理和极大极小不等式

M·巴拉奇

奥拉迪亚大学数学系,奥拉迪亚 410087,罗马尼亚

详细信息

中图分类号: O189.1
计量
- 文章访问数: 3039
- HTML全文浏览量: 106
- PDF下载量: 640
- 被引次数: 0
出版历程
- 收稿日期: 2007-08-16
- 修回日期: 2008-03-16
- 刊出日期: 2008-05-15

Alternative Principles and Minimax Inequalities in G-Convex Spaces

Mircea Balaj

Department of Mathematics, University of Oradea, 410087 Oradea, Romania

摘要

摘要: 利用Kuo、Jeng和Huang提出的不动点定理，给出G-凸空间中关于3个映射值的非常一般的相交定理．由此结果依次导出了关于极大元、解析择一和极大极小不等式的择一定理．
- G-凸空间 /
- 严格KKM性质 /
- 不动点定理 /
- 极大元 /
- 择一定理 /
- 极大极小不等式
Abstract: By using a fixed point theorem due to Kuo,Jeng and Huang in G-convex spaces a very general intersection theorem concerning the values of three maps was obtained.From this result successively alternative theorems concerning maximal elements,analytic alternatives and minimax inequalities were derived.
- G-convex space /
- strict KKM property /
- fixed point theorem /
- maximal element /
- alternative theorem /
- minimax inequality

HTML全文

参考文献(14)

[1]	Lassonde M. Fixed points for Kakutani factorizable multifunctions[J].J Math Anal Appl,1990,152(1):46-60. doi: 10.1016/0022-247X(90)90092-T
[2]	Tian C G. Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium,and complementarity[J].J Math Anal Appl,1992,170(2):457-471. doi: 10.1016/0022-247X(92)90030-H
[3]	Lin L J. Applications of a fixed point theorem in G-convex spaces[J].Nonlinear Anal,2001,46(5):601-608. doi: 10.1016/S0362-546X(99)00456-3
[4]	Kim H,Park S.Remarks on the KKM property for open-valued multimaps on generalized convex spaces[J].J Korean Math Soc,2005,42(1):101-110. doi: 10.4134/JKMS.2005.42.1.101
[5]	Park S. New subclases of generalized convex spaces[A].In:Fixed Point Theory and Applications[C].New York:Nova Sci Publ,2000,91-98.
[6]	Park S. Remarks on fixed point theorems in generalized convex spaces[A].In:Fixed Point Theory and Applications[C].New York: Nova Sci Publ,2000,135-144.
[7]	Watson P J. Coincidences and fixed points in locally G-convex spaces[J]. Bull Austral Math Soc,1999,59(2):297-304. doi: 10.1017/S0004972700032901
[8]	Kuo T Y,Jeng J C,Huang Y Y.Fixed point theorems for compact multimaps on almost G-convex sets in generalized convex spaces[J].Nonlinear Anal,2007,66(2):415-426. doi: 10.1016/j.na.2005.11.036
[9]	Chang T H, Yen C L.KKM property and fixed point theorems[J].J Math Anal Appl,1996，203(1): 224-235. doi: 10.1006/jmaa.1996.0376
[10]	Nikodem K. K-convex and K-concave set-valued functions[R]. Politechnika Lodzka, 1989.
[11]	Ding X P. Coincidence theorems and equilibria of generalized games[J]. Indian J Pure Appl Math,1996,27(11):1057-1071.
[12]	Balaj M. Minimax inequalities in G-convex spaces[J].Bull Austral Math Soc，2005,71(3):367-376. doi: 10.1017/S0004972700038363
[13]	Balaj M. Two minimax inequalities in G-convex spaces[J].Appl Math Lett,2006,19(3): 235-239. doi: 10.1016/j.aml.2005.06.003
[14]	Balaj M, Lin L J. Alternative theorems and minimax inequalities in G-convex spaces[J].Nonlinear Anal,2007,67(5):1474-1481. doi: 10.1016/j.na.2006.06.056