• 제목/요약/키워드: open-valued KKM theorem.

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REMARKS ON THE KKM PROPERTY FOR OPEN-VALUED MULTIMAPS ON GENERALIZED CONVEX SPACES

  • KIM HOONJOO;PARK SEHIE
    • 대한수학회지
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    • 제42권1호
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    • pp.101-110
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    • 2005
  • Let (X, D; ${\Gamma}$) be a G-convex space and Y a Hausdorff space. Then $U^K_C$(X, Y) ${\subset}$ KD(X, Y), where $U^K_C$ is an admissible class (dup to Park) and KD denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, a fixed point theorem, and a coincidence theorem.

COMMENTS ON GENERALIZED R-KKM TYPE THEOREMS

  • Park, Se-Hie
    • 대한수학회논문집
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    • 제25권2호
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    • pp.303-311
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    • 2010
  • Recently, some authors [3, 4, 11, 12, 15] adopted the concept of the so-called generalized R-KKM maps which are used to rewrite known results in the KKM theory. In the present paper, we show that those maps are simply KKM maps on G-convex spaces. Consequently, results on generalized R-KKM maps follow the corresponding previous ones on G-convex spaces.

MATCHING THEOREMS AND SIMULTANEOUS RELATION PROBLEMS

  • Balaj, Mircea;Coroianu, Lucian
    • 대한수학회보
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    • 제48권5호
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    • pp.939-949
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    • 2011
  • 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.

Coincidences of composites of u.s.c. maps on h-spaces and applications

  • Park, Seh-Ie;Kim, Hoon-Joo
    • 대한수학회지
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    • 제32권2호
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    • pp.251-264
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    • 1995
  • Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

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