<em>H</em>-度量空间中的广义KKM定理及其应用

H-度量空间中的广义KKM定理及其应用

基金项目: 国家自然科学基金资助项目(19871059)

摘要: 定义了一个新的空间——H-度量空间并在H-度量空间中,得到了具有有限度量紧闭(开)值的广义H-KKM映象的广义H-KKM定理。这些定理推广了 Khamsi和Yuan最近一系列结果。作为应用,还得到有限度量紧闭(开)覆盖的KyFan型匹配定理,不动点定理和极小极大不等式。这些结果统一和推广了近期的许多结果。
- 超凸空间 /
- H-度量空间 /
- 存限度量紧闭(开)集 /
- 广义H-KKM映象 /
- 容许集
Abstract: The new notions of H-metric spaces and generalized H-KKM mappings were introduced.Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces.These theorems generalize recent results of Khamsi and Yuan.As applications,some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers,fixed point theorems and minimax inequality are obtained in H-metric spaces.These results generalize a number of known results in recent literature.
- hyperconvex space /
- H-metric space /
- finitely metrically compactly closed (open) set /
- generalized H-KKM mapping /
- admissible set

[1]	Khamsi M A.KKM and Ky Fan theorem in hyperconvex spaces[J].J Math Anal Appl,1996,204(2):298-306.
[2]	Yuan X Z.The characterization of generalized metric KKM mappings with open values in hyperconvex metric spaces and some applications[J].J Math Anal Appl,1999,235(2):315-325.
[3]	Yuan X Z.KKM Theory and Applications in Nonlinear Analysis[M].New York:Marcel Dekker Inc,1999.
[4]	Aronszajn N,Panitchpakdi P.Extensions of uniformly continuous transformations and hyperconvex metric spaces[J].Pacific J Math,1956,6:405-439.
[5]	Bardaro C,Ceppitelli R.Some further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities[J].J Math Anal Appl,1988,132(3):484-490.
[6]	Horvath C.Extension and selection theorems in topological spaces with a generalized convexity structure[J].Ann Fac Sci Toulouse Math,1993,2:253-269.
[7]	张石生.变分不等式和相补问题理论及应用[M].上海:上海科技文献出版社,1991.
[8]	Horvath C.Some result on multivalued mapping and inequalities without convexity[A].In:Lin,Simons Eds.Nonlinear and Convex Analysis[C].New York:Marcel Dekker Inc,1987,96-106.
[9]	Ding X P,Tan K K.Matching theorems,fixed point theorems and minimax inequalities without convexity[J].J Austral Math Soc,Ser A,1990,49(1):111-128.
[10]	DING Xie-ping.Fixed points minimax inequalities and equilibria of noncompact abstract economies[J].Taiwanese J Math,1998,2(1):25-55.