Vol. 56, No. 1, 1975

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On the extremal elements of the convex cone of superadditive n-homogeneous functions

Melvyn W. Jeter

Vol. 56 (1975), No. 1, 131–141

Let Pn be the collection of finite-valued functions defined on the nonnegative orthant, En2+, of euclidean n2-space such that for p Pn it follows that p : En2+ E1+ and in addition

(a) p is continuous,

(b) p(αx) = αnp(x)0,

(c) p(x + y) p(x) + p(y).

It follows readily that Pn is closed with respect to addition and nonnegative scalar multiplication. Therefore, Pn is a convex cone, whose vertex is the zero function, in the linear space of real functions defined on En2+. The purpose of this paper is to investigate the extremal elements of Pn.

Mathematical Subject Classification 2000
Primary: 46A40
Received: 15 October 1973
Revised: 16 May 1974
Published: 1 January 1975
Melvyn W. Jeter