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KKM技巧及其应用

张石生 马意海

张石生, 马意海. KKM技巧及其应用[J]. 应用数学和力学, 1993, 14(1): 9-18.
引用本文: 张石生, 马意海. KKM技巧及其应用[J]. 应用数学和力学, 1993, 14(1): 9-18.
Zhang Shi-sheng, Ma Yi-hai. KKM Technique and Its Applications[J]. Applied Mathematics and Mechanics, 1993, 14(1): 9-18.
Citation: Zhang Shi-sheng, Ma Yi-hai. KKM Technique and Its Applications[J]. Applied Mathematics and Mechanics, 1993, 14(1): 9-18.

KKM技巧及其应用

KKM Technique and Its Applications

  • 摘要: 本文介绍KKM技巧,并用以建立了新的抉择定理和重合定理,它们是[2,10,11,15,16]等近期文献中一些重要结果的推广.
  • [1] Baiocchi,C.and A.Capelo,Variational and Quasi-variational Inequalities,John Wiley and Sons(1984).
    [2] Bardaro,C.and R.Ceppitelli,Applications of the generalized Knaster-Kuratowski-Mazurkiewiez theorem to variational inequalities,J.Math.Anal.Appl.,137(1989),46-58.
    [3] Browder,F,E.,The fixed point theory of multivalued mappings in topological vector spaces,Math.Ann.,177(1968),283-301.
    [4] Chang Shih-sen and Chang Yin,Generalized KKM theorem and variational inequalities,J.Math.Anal.Appl.(in print).
    [5] Dugundji,J.and A.Granas,Fixed Point Theory,Vol.Ⅱ,Warszawa(1982).
    [6] Fan,K.,A generalization of Tychonoffs fixed point theorem,Math.Ann.142(1961),305-310.
    [7] Fan,K.,Some properties of convex sets related to fixed point theorems,Math.Ann.,266(1984),519-537.
    [8] Granas,A.,KKM-maps and their applications to nonlinear problems,The Scottish Book(Mathematics from Scottish Cafe),Edited by R.D.Mauldin,Birkhäuser,Boston(1982).
    [9] Ha,C:-W.,On a minimax inequality of Ky Fan,Proc.Amer.Math.Soc.,99,4(1987),680-682.
    [10] Horvath,C.,Some results on multivalued mappings and inequalities without convexity,Nonlinear and Convex Analysis,Lecture Notes in Pure and Appl.Math.,Series 107(1987).
    [11] Jiang Jia-he,Coincidence theorems and minimax theorems,Acta Mathematica Sinica,New Series,5,4(1989),307-320.
    [12] Knaster,B.,K.Kuratowski and S.Mazurkiewicz,Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe,Fund.Math.,14(1929),132-137.
    [13] Lassonde,M.,On the use of KKM multifunctions in fixed point theory and related topics,J.Math.Anal.Appl.,97(1983),151-201.
    [14] Mazur,S.and J.Schauder,Über ein Prinzip in der Variationsrechnung,Proc.Int.Congress Math.,10(1936),65.
    [15] Park,S.,Generalizations of Ky Fan's matching theorems and their applications,J.Math.Anal.Appl.,141(1989),164-176.
    [16] Shih,M.-H.and K.-K.Tan,A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems,J.Austral.Math.Soc.,Series A,45(1988),169-183.
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出版历程
  • 收稿日期:  1991-11-06
  • 刊出日期:  1993-01-15

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