On new majorization theorems
type: Item
instance of: scholarly article
title: On new majorization theorems
zbMATH Open document ID: 0906.26015
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-01-25T00:00:00Z
full work available at URL: CONT27-3.html
review text: Several majorization theorems of the following type are proved: Let \(g\) be a strictly increasing function from \((a,b)\) to \((c,d)\), \(f\) be an increasing function on \((a,b)\) and \(f\circ g^{-1}\) be a concave function on \((c,d)\). If the vectors \({\mathbf x}\) and \({\mathbf y}\) with elements from \((a,b)\) satisfy \[ \sum_{i=1}^kw_ig(x_i)\geq\sum_{i=1}^kw_ig(y_i), \qquad k=1,\dots,n, \] and the vector \(\mathbf x\) is increasing, then \[ \sum_ {i=1}^kw_if(x_i)\geq\sum_{i=1}^kw_if(y_i),\qquad k=1,\dots,n. \] Some applications are also given.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1143475
zbMATH Keywords: majorization
zbMATH Keywords: inequalities
author: J. Pečarić
author: S. Abramovich
reviewed by: Gheorghe Toader
MaRDI profile type: Publication
OpenAlex ID: W2093006010
cites work: Majorization, doubly stochastic matrices, and comparison of eigenvalues
cites work: Q3759073
cites work: Weighted Favard and Berwald inequalities
cites work: Inequalities: theory of majorization and its applications
cites work: Convex functions, partial orderings, and statistical applications
cites work: Q4697396
DOI: 10.1216/RMJM/1181071901
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description: scientific article; zbMATH DE number 1143475