Fixed points in nonconvex domains
Eric Chandler, Gary D. Faulkner · Proceedings of the American Mathematical Society · 1980
A lemma of Janos is used to prove that nonexpansive self-maps which “shrink” a compact set X away from its boundary in co ¯ X \overline {{\text {co}}} \;X have fixed points in X . The lemma is further employed to derive a version, for nonexpansive maps on star-shaped sets, of Janos and Solomon’s fixed-point theorem for continuous maps on spaces having an attractor for compact sets.