• Title/Summary/Keyword: hyperconvex metric space

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FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.885-899
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    • 2000
  • We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

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A MISCELLANY OF SELECTION THEOREMS WITHOUT CONVEXITY

  • Kim, Hoonjoo
    • Honam Mathematical Journal
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    • v.35 no.4
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    • pp.757-764
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    • 2013
  • In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.