A geometric mean of parameterized arithmetic and harmonic means of convex functions
type: Item
instance of: scholarly article
title: A geometric mean of parameterized arithmetic and harmonic means of convex functions
zbMATH Open document ID: 1256.90035
DOI: 10.1155/2012/836804
author: Sangho Kum
author: Yongdo Lim
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: The notion of the geometric mean of two positive reals was extended by Ando in 1978 to the case of positive semidefinite matrices \(A\) and \(B\). Moreover, an interesting generalization of the geometric mean \(A \sharp B\) of \(A\) and \(B\) to convex functions was introduced by \textit{M. Atteia} and \textit{M. Raïssouli} [J. Convex Anal. 8, No. 1, 223--240 (2001; Zbl 1003.90030)] with a different viewpoint of convex analysis. The present work aims at providing a further development of the geometric mean of convex functions due to Atteia and Raïssouli [loc. cit.]. A new algorithmic self-dual operator for convex functions named ``the geometric mean of parameterized arithmetic and harmonic means of convex functions'' is proposed, and its essential properties are investigated.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 6134171
Wikidata QID: Q58696900
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/836804
OpenAlex ID: W1971680150
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description: scientific article; zbMATH DE number 6134171