<em>H</em>-空间的覆盖性质及其应用

丁协平; 陈国强

H-空间的覆盖性质及其应用

丁协平¹,
陈国强²

1.
四川师范大学成都;
2.
达尔豪斯大学加拿大

基金项目: 国家自然科学基金资助项目;加拿大NSERC资助项目

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- 被引次数: 0
出版历程
- 收稿日期: 1992-05-25
- 刊出日期: 1993-12-15

Covering Properties of H Spaces and Applications

Ding Xie-ping¹,
Tan Kok-keong²

1.
Department of Mathematics, Sichuan Normal University, Chengdu;
2.
Department of Mathematics, Statistics and Computing Science Dalhousie University, Halifax, Nova Scotia, Canada

摘要

摘要: 我们得到了H-空间闭(开)覆盖性质的几个定理,改进和推广了Sperner.Klee,Alexandroff-Pasynkoff,Berge,Ghouila-Houri,Danzer-Grunbaum-Klee,Ky Fan,Shih-Tan,Horvath和Lassonde等人的相应结果.作为应用,我们对l.c.-空间内的下半连续集值映象证明了一个几乎不动点定理并且推广吉洪诺夫不动点定理到l.c.-空间.这些定理改进了Ky Fan和Horvath的相应结果.
- 覆盖性性 /
- H-空间 /
- l.c.-空间 /
- 几乎不动点
Abstract: Several theorems on closed(resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
- covering property /
- H-space /
- H-convex /
- H-convex hull

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参考文献(20)

[1]	Alexandroff,P.and B.Pasynkoff,Elementary proof of the essentiality of the identical mapping of a simplex,Uspehi Mat.Nauk(N.S.),12,5(77)(1957),175-179.(in Russian)
[2]	Bardaro,C.and R.Ceppitelli,Some further generalizations of Knaster-Kuratowski-Ma-zurkiewicz theorem and minimax inequalities,J.Math.Anal.Appl.,132(1988),484-490.
[3]	Berge,C.,Espace Topologiques,Fonctions Multivogues,Dunod,Paris(1959).
[4]	Berge,C.,Sur une propriete combinatoire des ensembles convexes,C.R.Acad.Sci.Paris,248(1959),2698-2699.
[5]	Danzer,L.,B.Gr黱baum and V.Klee,Helly's theorem and its relatives,convexity.Proc.Sympos.Pure Math.7,Edited by V.Klee,Amer.Math.Soc.Providence,RI(1963),101-177.
[6]	Ding,X.P.and K.K.Tan,Matching theorems,fixed point theorems and minimax inequalities without convexity,J.Austral.Math.Soc.(Ser.A),49(1990),111-128.
[7]	Fan,K.,A covering property of simplexes,Math.Scand.,22(1968),17-20.
[8]	Fan,K.,A combinatorial property of pseudomanifolds and covering properties of simplexes,J.Math.Anal.Appl.,31(1970),68-80.
[9]	Fan,K.,Covering properties of convex sets and fixed point theorems in topological vector spaces,Sympos.on Infinite Dimensional Topology,Ed.by R.D.Anderson,Princeton(1972),79-92.
[10]	Ghouila-Houri,A.,Sur letude combinatoire des families de convexes,C.R.Acad.Sci.Paris,252(1961),494-496.
[11]	Horvath,C.,Some results on multivalued mappings and inequalities without convexity,Nonlinear and Convex Analysis,Ed.by B.L.Lin and S.Simons,Marcel Dekker(1987),99-106.
[12]	Horvath,C.,Contractibility and generalized convexity,J.Math.Anal.Appl.,156(1991),341-357.
[13]	Idzik,A.and K.K.Tan,Covering properties of simplexes,J.Math.Anal.Appl.(to appear)
[14]	Klee,V.L.,On certain intersection properties of convex sets,Canada J.Math.,3(1951),272-275.
[15]	Knaster,B.,C.Kuratowski and S.Mazurkiewicz,Ein beweis des Fixpunktsatzes f黵 n-dimensionale Simplexe,Fund.Math.,14(1929).132-137.
[16]	Lassonde,M.,Sur le principe KKM,C.R.Acad.Sci.Paris,Ser 1310(1990),573-576.
[17]	Shih,M.H.and K.K.Tan,Covering theorems of simplexes and system of linear inequalities,Linear and Multilinear Algehra,19(1986),309-320.
[18]	Sperner,E.,Neuer beweis f黵 die invarianz der dimensions-zahl und des gebietes,Abh.Math.Sem.Univ.Hamburg,6(1928),265-272.
[19]	Tarafdar,E.,A fixed point theorem in H-space and related results,Bull.Austral.Math.Soc.,42(1990),133-140.
[20]	Tychonoff,A.,Ein Fixpunktsatz,Math.Annalen,111(1935),767-776.