Coordinatewise star-shaped sets in c0

In 1981, R. Haydon, E. Odell, and Y. Sternfeld [R. Haydon, E. Odell, Y. Sternfeld, A fixed point theorem for a class of star-shaped sets in c0, Israel J. Math. 38 (1–2) (1981) 75–81] proved that weakly compact, coordinatewise star-shaped sets in c0 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