Some generalizations of real power form for Young-type inequalities and their applications
type: Item
instance of: scholarly article
title: Some generalizations of real power form for Young-type inequalities and their applications
zbMATH Open document ID: 1505.26029
author: Duong Quoc Huy
author: Doan Thi Thuy Van
author: Dinh Thi Xinh
published in: Linear Algebra and its Applications
publication date: 2022-11-08T00:00:00Z
review text: The weighted arithmetic-geometric means inequality \[ \nu a+(1-\nu)b\geq a^\nu b^{1-\nu}\quad (a,b\geq0,\, \nu\in[0,1]) \] is known as the Young inequality. Among various generalizations of this inequality, it has been shown in [\textit{D. Choi}, Math. Inequal. Appl. 21, No. 1, 99--106 (2018; Zbl 1386.15041)] that \[ (\nu a+(1-\nu)b)^m\geq \left(a^\nu b^{1-\nu}\right)^m+(2r_0)^m\left(\left(\frac{a+b}{2}\right)^m-(ab)^{m/2}\right) \] holds for any positive integer \(m\), where \(r_0=\min\{\nu,1-\nu\}\). In the present paper, the authors utilize majorization techniques to prove the above inequality in the case where \(m\) is replaced with a real number \(p\geq 1\). Some operator versions are presented as well.
reviewed by: Mohsen Kian
Mathematics Subject Classification ID: 26D07
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 7613300
zbMATH Keywords: Young inequality
zbMATH Keywords: weak majorization
zbMATH Keywords: operator inequality
MaRDI profile type: Publication
full work available at URL: j.laa.2022.10.003
OpenAlex ID: W4302362966
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DOI: 10.1016/J.LAA.2022.10.003
description: scientific article; zbMATH DE number 7613300