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H-空间的覆盖性质及其应用

丁协平 陈国强

丁协平, 陈国强. H-空间的覆盖性质及其应用[J]. 应用数学和力学, 1993, 14(12): 1025-1033.
引用本文: 丁协平, 陈国强. H-空间的覆盖性质及其应用[J]. 应用数学和力学, 1993, 14(12): 1025-1033.
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.

H-空间的覆盖性质及其应用

基金项目: 国家自然科学基金资助项目;加拿大NSERC资助项目

Covering Properties of H Spaces and Applications

  • 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.
  • [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).
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    [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.
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    [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.
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    [18] Sperner,E.,Neuer beweis f黵 die invarianz der dimensions-zahl und des gebietes,Abh.Math.Sem.Univ.Hamburg,6(1928),265-272.
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出版历程
  • 收稿日期:  1992-05-25
  • 刊出日期:  1993-12-15

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