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

Abstract

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
Volume128
Issue number11
DOIs
StatePublished - 2000

Keywords

  • Fixed points
  • Hyperconvex metric spaces
  • Selection theorems

Fingerprint

Dive into the research topics of 'Fixed point and selection theorems in hyperconvex spaces'. Together they form a unique fingerprint.

Cite this