Tangent cones, starshape and convexity

In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets [14] have been made. These began with a paper by Edelstein and Keener [8] and have culminated in the papers by Borwein, Edelstein and O'Brien [3] [4] by Edelstein, Keener and O'Brien [9] and finally by O'Brien [16].