Fixed point and selection theorems in hyperconvex spaces

M. A. Khamsi, W. A. Kirk, Carlos Martinez Yañez

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


It is shown that a set-valued mapping T*of a hyperconvex metric space M which takes values in the space of nonempty externally hyperconvex subsets of M always has a lipschitzian single valued selection T which satisfies d(T(x),T(y)) ≤ dH(T*(x),T*(y)) for all x,y 6 ε. (Here dH denotes the usual Hausdorff distance.) This fact is used to show that the space of all bounded λ-lipschitzian self-mappings of M is itself hyperconvex. Several related results are also obtained.

Original languageBritish English
Pages (from-to)3275-3283
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number11
StatePublished - 2000


  • Fixed points
  • Hyperconvex metric spaces
  • Selection theorems


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