Converses of two inequalities of Ky Fan, O. Taussky, and J. Todd
type: Item
instance of: scholarly article
title: Converses of two inequalities of Ky Fan, O. Taussky, and J. Todd
zbMATH Open document ID: 0747.26014
DOI: 10.1016/0022-247X(91)90365-7
author: Horst Alzer
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: Simple new proofs of the following inequalities of G. V. Milovanović and I. Ž. Milovanović are given: \[ \sum^{n+1}_{k=1}(a_ k- a_{k-1})^ 2\leq 2\left(1+\cos{\pi\over n+1}\right)\sum^ n_{k=1}a_ k^ 2, \leqno (1) \] which holds for all real numbers \(a_ 0=0\), \(a_ 1,\ldots,a_ n\), \(a_{n+1}=0\), and \[ \sum^ n_{k=1}(a_ k-a_{k-1})^ 2\leq 2\left(1+\cos{2\pi\over 2n+1}\right)\sum^ n_{k=1}a^ 2_ k, \leqno (2) \] which is valid for all real numbers \(a_ 0=0\), \(a_ 1,\ldots,a_ n\). The constants \(2\left(1+\cos{\pi\over n+1}\right)\) and \(2\left(1+\cos{2\pi\over 2n+1}\right)\) given in (1) and (2), respectively, are best possible.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 57296
zbMATH Keywords: discrete inequalities of Wirtinger's type
zbMATH Keywords: inequality of Ky Fan
zbMATH Keywords: inequality of O. Taussky and J. Todd
reviewed by: J. Pečarić
MaRDI profile type: Publication
cites work: Q3658220
cites work: Discrete analogs of inequalities of Wirtinger
cites work: On discrete inequalities of Wirtinger's type
cites work: Q3689399
full work available at URL: 0022-247x(91)90365-7
OpenAlex ID: W1974574085
description: scientific article; zbMATH DE number 57296