Coordinatewise star-shaped sets in c0

Abstract

A fixed point theorem for a class of star-shaped sets in c 0 , Israel J. Math. 38 (1-2) (1981) 75-81] proved that weakly compact, coordinatewise star-shaped sets in c 0 have the fixed point property for nonexpansive mappings. In this article, it is shown that, for closed, bounded, coordinatewise star-shaped sets, the fixed point property is equivalent to weak compactness.