Covering Properties of H Spaces and Applications

Ding Xie-ping; Tan Kok-keong

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Ding Xie-ping, Tan Kok-keong. Covering Properties of H Spaces and Applications[J]. Applied Mathematics and Mechanics, 1993, 14(12): 1025-1033.

Citation:

Ding Xie-ping, Tan Kok-keong. Covering Properties of H Spaces and Applications[J]. Applied Mathematics and Mechanics, 1993, 14(12): 1025-1033.

Citation:

Ding Xie-ping, Tan Kok-keong. Covering Properties of H Spaces and Applications[J]. Applied Mathematics and Mechanics, 1993, 14(12): 1025-1033.

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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

Received Date: 1992-05-25
Publish Date: 1993-12-15

Abstract

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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References(20)

References

[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.