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On the extremal
elements of the convex cone of superadditive n-homogeneous functions
Melvyn W. Jeter |
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Vol. 56 (1975), No. 1, 131–141
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Abstract |
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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),α ≧ 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
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Milestones
Received: 15 October 1973
Revised: 16 May 1974
Published: 1 January 1975
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Authors |
| Melvyn W. Jeter | |
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