A generalization of the Arrow-Barankin-Blackwell theorem in normed spaces
type: Item
instance of: scholarly article
title: A generalization of the Arrow-Barankin-Blackwell theorem in normed spaces
zbMATH Open document ID: 0734.49008
DOI: 10.1016/0022-247X(91)90265-2
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: Let X be a normed space and C a closed convex point cone in X, \(C^+=\{x^*\in X^*:\) \(x^*(c)\geq 0\) for every \(c\in C\}\), \(C^+_ 0=\{x^*\in X^*:\) \(x^*(c)>0\) for every \(c\in C\setminus \{0\}\}\), if \(S\subset X\) and \(x^*\in C^+_ 0\) we define \(P_ S(x^*)=\{s_ 0\in S:\) \(x^*(s_ 0)\leq x^*(s)\) for every \(s\in S\}\) and \(P_ S=\cup \{P_ S(x^*):\) \(x^*\in C^+_ 0\}\), Min S\(=\{s\in S:\) \((s- C)\cap S=\{s\}\}\). If the algebraic interior of \(C^+\) is a non empty set and S is a weakly compact convex set in X, then \(P_ S\subset Min S\subset w\)-cl \(P_ S\).
Mathematics Subject Classification ID: 49J99
zbMATH DE Number: 4214799
zbMATH Keywords: normed space
zbMATH Keywords: closed convex point cone
author: Francesco Ferro
reviewed by: Gianfranco Bottaro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214799