%0 Journal Article %T Conic structure of the non-negative operator convex functions on $(0,\infty)$ %A Uwe Franz %A Fumio Hiai %J Mathematics %D 2013 %I arXiv %X The conic structure of the convex cone of non-negative operator convex functions on $(0,\infty)$ (also on $(-1,1)$) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone. %U http://arxiv.org/abs/1310.1539v2