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AIMS Mathematics

2021, Volume 6, Issue 4: 3160-3176. doi: 10.3934/math.2021191
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Strongly essential set of vector Ky Fan's points problem and its applications

  • 1.
    School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou 550025, China
  • 2.
    School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550025, China
  • 3.
    College of Mathematical and Information Science, Guiyang University, Guiyang, Guizhou 550005, China
  • 4.
    School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, China
  • Received: 12 November 2020 Accepted: 05 January 2021 Published: 15 January 2021

  • MSC : 46T20, 49J53, 91A10

  • In this paper, several existence results of strongly essential set of the solution set for Ky Fan's section problems and vector Ky Fan's point problems are obtained. Firstly, two kinds of strongly essential sets of Ky Fan's section problems are defined, and some further results on existence of the strongly essential component of solutions set of Ky Fan's section problems are proved, which generalize the conclusion in [22], and further generalize the conclusions in [21,28]. Secondly, based on the above results, two classes of stronger perturbations of vector-valued inequality functions are proposed respectively, and several existence results of the strongly essential component of set of vector Ky Fan's points are obtained. By comparing several metrics, we give some strong and weak relationships among the various metrics involved in the text. The main results of this paper actually generalize the relevant conclusions in the current literature. Finally, as an application, we obtain an existence result of the strongly essential component of weakly Pareto-Nash equilibrium for multiobjective games.

    Citation: Dejin Zhang, Shuwen Xiang, Xicai Deng, Yanlong Yang. Strongly essential set of vector Ky Fan's points problem and its applications[J]. AIMS Mathematics, 2021, 6(4): 3160-3176. doi: 10.3934/math.2021191

    Related Papers:

  • In this paper, several existence results of strongly essential set of the solution set for Ky Fan's section problems and vector Ky Fan's point problems are obtained. Firstly, two kinds of strongly essential sets of Ky Fan's section problems are defined, and some further results on existence of the strongly essential component of solutions set of Ky Fan's section problems are proved, which generalize the conclusion in [22], and further generalize the conclusions in [21,28]. Secondly, based on the above results, two classes of stronger perturbations of vector-valued inequality functions are proposed respectively, and several existence results of the strongly essential component of set of vector Ky Fan's points are obtained. By comparing several metrics, we give some strong and weak relationships among the various metrics involved in the text. The main results of this paper actually generalize the relevant conclusions in the current literature. Finally, as an application, we obtain an existence result of the strongly essential component of weakly Pareto-Nash equilibrium for multiobjective games.


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