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Another form of KKM type theorem and its applications on generalized convex spaces

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Abstract

In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications. The main results improve and generalize the corresponding results in previous papers.

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References

  1. Knaster, B, Kuratowski, K, Mazurkiewicz S. Ein beweis des Fixpunktsatzes für n-dimensionale simplexe, Fund Math, 1929, 14:132–137.

    Google Scholar 

  2. Park S. Elements of the KKM theory for generalized convex spaces, Korean J Comp Appl Math, 2000, 7(1):1–28.

    MATH  Google Scholar 

  3. Fan Ky. A generalization of Tychonoff's fixed point theorem Math Ann, 1961, 142:305–310.

    Article  MATH  MathSciNet  Google Scholar 

  4. Lassonde M. On the use of KKM multimaps in fixed point theory and related topics, J Math Anal Appl, 1983, 97:151–201.

    Article  MATH  MathSciNet  Google Scholar 

  5. Horvath C D. Contractibility and generalized convexity, J. Math Anal Appl, 1991, 156:341–357.

    Article  MATH  MathSciNet  Google Scholar 

  6. Park S, Kim H J. Foundations of the KKM theory on generalized convex spaces, J. Math Anal Appl, 1997, 209:551–571.

    Article  MATH  MathSciNet  Google Scholar 

  7. Park S. New susclasses of generalized concex spaces. In: Cho Y J ed. Fixed Point Theory and Applications, New York: Nova Sci Publ, 2000, 91–98.

    Google Scholar 

  8. Liu F C. On a form of KKM principle and supinfsup inequalities of von Neumann and Fan Ky type, J Math Anal Appl, 1991, 155:420–436.

    Article  MATH  MathSciNet  Google Scholar 

  9. Li H M, Ding X P. On versions of KKM principle in H-spaces and its appications, J Sichuan Normal Univ, 1993, 16(3):21–27.

    MATH  MathSciNet  Google Scholar 

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Supported by the National Natural Science Foundation of China (10361005).

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Yongjie, P., Xuelian, J. Another form of KKM type theorem and its applications on generalized convex spaces. Appl. Math.- J. Chin. Univ. 21, 207–213 (2006). https://doi.org/10.1007/BF02791346

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  • DOI: https://doi.org/10.1007/BF02791346

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