Zhang Shi-sheng, Wu Xian. Topologicai Version of Section Theorems with Applications[J]. Applied Mathematics and Mechanics, 1995, 16(2): 123-131.
Citation: Zhang Shi-sheng, Wu Xian. Topologicai Version of Section Theorems with Applications[J]. Applied Mathematics and Mechanics, 1995, 16(2): 123-131.

Topologicai Version of Section Theorems with Applications

  • Received Date: 1994-04-04
  • Publish Date: 1995-02-15
  • In this paper some new types of KKM theorem and section theorems are given.As applications,the existence problems of solutions for three kinds of variational inequalities and fixed point problem for set-valued mapping have been siudied by usingthose results.The results presented in this paper improve and extend the main resultsin [1-19].
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  • [1]
    Bardaro,C.and R.Ceppitelli,Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities,J.Math.Anal.Appl.,132(1988),484-490.
    [2]
    Bardaro,C.and R.Ceppitelli,Applications of generalized Knaster-Kuratowski-Mazukiewicz theorem to variational inequalites,J.Math.Anal.Appl.,137(1989),46-58.
    [3]
    Bardaro,C.and R.Ceppitelli,Fixed point theorems and vector-valued minimax theorems,J.Math.Anal.Appl.,146(1990).363-373.
    [4]
    Browder,F:E.,A new generalization of the Schauder fixed point theorem,Math.Ann.,174(1967).285-290.
    [5]
    Browder,F.E.,The fixed point theory of multi-valued mappings in topological vector space,Math.Ann.,177(1968),283-301.
    [6]
    Chang Shih-sen and Ma Yi-hai,Generalized KKM theorem on H-space with applications,J.Math.Anal.Appl.163(1992),406-421.
    [7]
    Chang Shih-sen and Zhang Ying,cieneralized KKM theorem and variational inequalities,J.Math.Anal.Appl.,159(1991).208-223.
    [8]
    Fan,K.,A minimax inequality and applications,Inequalities Ⅲ,Ed.by O.Shisha.Academic Press,New York(1972),103-113.
    [9]
    Fan,K,Fixed point and related theorems for noncompact convex sets,Game Theory and Releated Topics,Eds.by O.Moeschlin and D.Pallaschke,North-Holland(1979),151-156.
    [10]
    Fan,K.,Some properties of convex of convex set related to fixed point theorems,Math.Ann.,266(1984).519-537.
    [11]
    Ko,H.M.and K.K.Tan,A coincidence theorem with application to minimax inequalities and fixed point theorems,Tamkang J.Math.,17(1986),37-43.
    [12]
    Lassonde,M.,On the use of KKM multifunctions in fixed point theory and related topics,J.Math.Anal.Appl.,97(1983),151-201.
    [13]
    Park,S.,Generalizations of Ky Fan's Matching theorems and their applications,J.Math.Anal.Appl.,141(1989),164-176.
    [14]
    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.
    [15]
    Shih,M.H.and K.K.Tan,The Ky Fan minimax principle,sets with convex sections and variational inequalities,DiJrerentia! Geometry-Calculus or Variational and Their Applicnrions,Eds.by M.Rassias and T.Rassia,New York(1985),471-481.
    [16]
    Takahashi,W.,Fixed point minimax and Hahu-Banach theorems,Proc.Suympos.Pure Math.,45.Part 2(1986).419-427.
    [17]
    Tan,K.K.,Comparison theorems on minimax inequalities,variational inequalities and fixed point theorems,J.London Math.Soc.,23(1983),555-562.
    [18]
    Yen,C.L.,A minimax inequality and its applications to variational inequalities,Pacific J.Math.,97(1981).477-481.
    [19]
    Gwinner,J.,On some fixed points and variational inequalities——A circular tour Nonliuenr Annl.,5.5(1981).565-583.
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