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 Technique and Its Applications

  • Received Date: 1991-11-06
  • Publish Date: 1993-01-15
  • In this paper, the Knaster-Kitrattnvski-Maiurkiewic: technique(KKM technique, in short) is presented. By using this technique a new alternative theorem ami a new coincidence theorem are estahlished. The results obtained in this paper unify and generalize the corresponding results in the recent works[2,10,11,15,16].
  • loading
  • [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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2443) PDF downloads(467) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return