Fixed points for nonexpansive mappings in Banach spaces
Pratheepa Jeganathan · Open University of Cape Town (University of Cape Town) · 1991
C is a nonempty bounded closed convex set with normal structure in a reflexive Banach space (L3.2);C is a nonempty closed convex (not necessarily bounded) set with normal structure in a reflexive Bana~ space such that the map has a bounded orbit (1.3.5);• C is nonempty, bounded closed and convex in a uniformly c?nvex Banach space (1.4.3);C is nonempty, bounded closed and convex with asymptotic normal structure in a reflexive Banach space (1.5.3).In addition, we al.so look at some results involving nonexpansive mappings in Hilbert spaces.Following this survey, we consider the special class of metric spaces known as hyperconvex spaces.This class is familiar to categ~rical topologists, but_ not so familiar t~ analysts.However, we will prove some important results involving nonexpansive mappings in .•But o(M) = 2 r(M) by 1.7.9 (ii).Thus o(M) = 0.