A general form of Alzer's inequality
type: Item
instance of: scholarly article
title: A general form of Alzer's inequality
zbMATH Open document ID: 1056.26016
DOI: 10.1016/S0898-1221(02)00155-4
author: Zengkun Xu
author: Dapeng Xu
publication date: 2004-11-18T00:00:00Z
review text: Alzer's inequality from 1993 states that \(S_n(r)/S_{n+1}(r)\geq (n/(n+ 1))^r\) for \(n= 1,2,\dots\); \(r> 0\), where \(S_n(r)= {1\over n}\sum^n_{i=1} i^r\). The first easy proof for Alzer's inequality has been obtained in 1995 by the reviewer, who used mathematical induction and Cauchy's mean value theorem of differential calculus. The authors now use this method to deduce generalizations for sequences of positive integers, satisfying certain auxiliary conditions.
reviewed by: József Sándor
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 2116473
zbMATH Keywords: Alzer inequality
zbMATH Keywords: generalization
zbMATH Keywords: mathematical induction
zbMATH Keywords: mean-value theorems
zbMATH Keywords: fractional inequalities
MaRDI profile type: Publication
cites work: Generalization of H. Alzer's inequality
cites work: On an inequality of H. Minc and L. Sathre
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2116473