Addendum to the paper: Fixed points for non-expansive set-valued mappings

  • J. Saint Raymond Université Paris 6, France


The aim of this paper is to improve or simplify some theorems which have been published in the paper ``Fixed points for non-expansive set-valued mappings"  in this journal after a stay of the author at the University of Catania. In particular in the previous paper the main results were that in general the known properties of the set of fixed points for contractive set-valued mappings fail as soon as one replaces ``contractive'' by ``non-expansive''. In fact, as we shall prove in this addendum, some of them hold true when the surrounding space is finite-dimensional, or the domain is compact. Some results of the previous paper are reproved here with a simpler proof for making this addendum more self-contained.