Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MATCHING THEOREMS AND SIMULTANEOUS RELATION PROBLEMS

  • Received : 2010.01.15
  • Published : 2011.09.30
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Abstract

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

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References

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