The fixed-point property under induced interval maps of continua - Robatian, D. (Нелінійні коливання, 2015)
Let f : I → I be a continuous map of a compact interval I and C(I) be the hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We investigate the existence of the fixed-point property of 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) has the fixed-point property.