An estimation of quasi-arithmetic mean by arithmetic mean and its applications
type: Item
instance of: scholarly article
title: An estimation of quasi-arithmetic mean by arithmetic mean and its applications
zbMATH Open document ID: 1120.47012
author: Masaru Tominaga
published in: Nihonkai Mathematical Journal
publication date: 2007-04-10T00:00:00Z
review text: For an increasing, strictly convex function \(f\) on an interval \(I\) and a selfadjoint operator \(A\) on a Hilbert space \(H\) whose spectrum is contained in \(I\), \(f^{-1}(\langle f(A)x, x\rangle)\geq \langle Ax,x\rangle\) is called the quasi-arithmetic mean inequality. In this paper, for each \(\lambda>0\), the author gives upper bounds for \[ f^{-1}(\langle f(A)x, x\rangle)-\lambda \langle Ax,x\rangle. \] Then the author derives some basic inequalities by looking at specific choices for \(f(t)\), such as \(t^p\), \(e^t\) and \(t\log t\).
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47A64
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5141505
zbMATH Keywords: quasi-arithmetic mean inequality
zbMATH Keywords: Specht ratio
zbMATH Keywords: logarithmic mean
zbMATH Keywords: generalized Kantorovich constant
zbMATH Keywords: determinant
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5141505