Inequalities of Furuta and Mond-Pečarić on the Hadamard product
type: Item
instance of: scholarly article
title: Inequalities of Furuta and Mond-Pečarić on the Hadamard product
zbMATH Open document ID: 0969.47016
DOI: 10.1155/S1025583400000138
author: Yuki Seo
author: S.-E. Takahasi
author: Jadranka Mićić
author: J. Pečarić
published in: Journal of Inequalities and Applications
publication date: 2001-01-30T00:00:00Z
full work available at URL: https://eudml.org/doc/121247
review text: In a previous paper [Math. Inequal. Appl. 2, No. 1, 83-111 (1999; Zbl 0924.47013)] the authors discussed inequalities of the form \[ (f(A)x, x)\leq\alpha g((Ax, x))+ \beta, \] where \(\alpha\) is a given real number and \(\beta\) is appropriately chosen. Here \(x\) is any unit vector and \(f\), \(g\) are real continuous functions, the first one convex. The present paper deals with similar inequalities over the Hadamard product. For instance, if \(A\), \(B\) are two strictly positive operators and \(f\) is a real, convex, supermultiplicative function one has for certain \(g\): \[ f(A)* f(B)\leq\alpha g(A* B)+\beta I. \] The inequality changes direction when \(f\) is concave.
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 1507755
zbMATH Keywords: inequalities
zbMATH Keywords: Hadamard product
zbMATH Keywords: supermultiplicative function
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1507755