Sections and extensions of concave functions
type: Item
instance of: scholarly article
title: Sections and extensions of concave functions
zbMATH Open document ID: 0619.90019
DOI: 10.1016/0304-4068(87)90021-8
author: Roger Howe
published in: Journal of Mathematical Economics
publication date: 1987-01-01T00:00:00Z
full work available at URL: d0760.pdf
review text: Necessary and sufficient conditions are given that a collection \(\phi_ i\), \(1\leq i\leq \ell\), of continuous, non-negative, concave functions on \({\mathbb{R}}^{n+}\) can all be realized as parallel sections of a single continuous, non-negative, concave function \(\psi\) on \({\mathbb{R}}^{m+}\), for some \(m\geq n\). This result shows at least the mathematical possibility of defining fundamental preferences in the sense of \textit{S.- Ch. Kolm} [''Justice et equité'', CNRS, Paris (1972)]. An analogous result for quasi-convex functions is also proved.
Mathematics Subject Classification ID: 91B99
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 4005947
zbMATH Keywords: sections
zbMATH Keywords: extensions
zbMATH Keywords: concave functions
zbMATH Keywords: Necessary and sufficient conditions
zbMATH Keywords: fundamental preferences
MaRDI profile type: Publication
OpenAlex ID: W2017617734
cites work: Q3226265
cites work: Convex Analysis
cites work: Equality of Resources Implies Equality of Welfare
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description: scientific article; zbMATH DE number 4005947