Bulletin of the Australian Mathematical Society

Research Article

Dominated extensions of functionals and V-convex functions of cancellative cones

S. Romagueraa1, E. A. Sánchez Péreza1 and O. Valeroa1

a1 Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: sromague@mat.upv.es, easancpe@mat.upv.es, ovalero@mat.upv.es

Abstract

Let C be a cancellative cone and consider a subcone C0 of C. We study the natural problem of obtaining conditions on a non negative homogeneous function φ: CR+ so that for each linear functional f defined in C0 which is bounded by φ, there exists a linear extension to C. In order to do this we assume several geometric conditions for cones related to the existence of special algebraic basis of the linear span of these cones.

(Received May 13 2002)