On the extremal elements of the convex cone of superadditiven-homogeneous functions

Let P n be the collection of finite-valued functions defined on the nonnegative orthant, E * 2 , of euclidean n 2 -space such that for p E P n it follows that p: Elr--> E\ and in addition (a) p is continuous, (b) p(ax) = a n p(x),a ^0, (c) It follows readily that P n is closed with respect to addition and nonnegative scalar multiplication. Therefore, P n is a convex cone, whose vertex is the zero function, in the linear space of real functions defined on E + n -. The purpose of this paper is to investigate the extremal elements of P*.