Journal of Mathematical Sciences

, Volume 215, Issue 3, pp 376–386 | Cite as

The Fixed-Point Property Under Induced Interval Maps of Continua

  • D. Robatian

Let f : I → I be a continuous map of a compact interval I and let C(I) be hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We study the fixed-point property of the subsets of C (I) with respect to any induced interval map ℱ : C (I) → C (I). In particular, we prove that any nonempty subcontinuum of C (I) possesses the fixed-point property.


Compact Interval Connected Subset Monotone Sequence Lower Vertex Compact Subinterval 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • D. Robatian
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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