Some relations between linear mappings and conjugations in idempotent analysis
type: Item
instance of: scholarly article
title: Some relations between linear mappings and conjugations in idempotent analysis
zbMATH Open document ID: 1055.49021
DOI: 10.1023/A:1023244401023
author: Ivan Singer
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-09-16T00:00:00Z
review text: The author proves a large number of results showing that the theory of {lower semicontinuous dioid-valued linear mappings} in [\textit{V. N. Kolokoltsov} and \textit{V. P. Maslov}, ``Idempotent analysis and its applications'', Appendix by Pierre Del Moral, transl. from the Russian by V. E. Nazaikinskij, Dordrecht (1997; Zbl 0941.93001)] is closely related to the {theory of the abstract Fenchel-Moreau conjugations for functions with values in extensions of completely ordered groups} studied by \textit{J.-E. Martínez-Legaz} and \textit{I. Singer} [{Optimization} {21}, No. 4, 481--508 (1990; Zbl 0728.90071); ibid. {22}, No. 4, 483--511 (1991; Zbl 0728.06007); ibid. {30}, No. 4, 295--315 (1994; Zbl 0815.49026); {Positivity} {1}, No. 3, 193--218 (1997; Zbl 0899.49016), etc.].
reviewed by: Ştefan Mirică
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 1982007
zbMATH Keywords: idempotent analysis
zbMATH Keywords: abstract conjugation
zbMATH Keywords: dioid
zbMATH Keywords: idempotent semiring
zbMATH Keywords: idempotent semifield
zbMATH Keywords: l.s.c. dioid-valued linear mapping
zbMATH Keywords: complete lattice-ordered group
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1982007