Refinements and extensions of an inequality. II
type: Item
instance of: scholarly article
title: Refinements and extensions of an inequality. II
zbMATH Open document ID: 0932.26010
author: Feng Qi
author: Senlin Xu
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-02-23T00:00:00Z
review text: By using certain known results for absolutely monotonic and absolutely convex functions, as well as classical integral inequalities, the following result is deduced: \[ (b^{x+ k}- a^{x+k})/(b^x- a^x)\geq {x+ k\over x} \Biggl({a+ b\over 2}\Biggr)^k, \] where \(k\geq 1\), \(x\geq 1\), \(0<a<b\) are real numbers. For \(0< k< 1\) or \(0< x< 1\), this inequality is not generally true. [See also Part III, J. Math. Anal. Appl. 227, No. 2, 439-448 (1998; following review); Part I has not yet been received by Zbl ].
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1053443
zbMATH Keywords: absolutely monotonic and absolutely convex functions
zbMATH Keywords: integral inequalities
reviewed by: József Sándor
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5318
OpenAlex ID: W2781649854
cites work: Q3999482
cites work: Q5287501
DOI: 10.1006/JMAA.1997.5318
Recommended article: Refinements and extensions of an inequality
Recommended article: Refinements and extensions of an inequality. III
Recommended article: Q5062575
Recommended article: Remark on refinements and extensions of an inequality
Recommended article: Extensions of some inequalities
Recommended article: Q3353290
Recommended article: On refinements of Hölder's inequality. II
Recommended article: Q4356764
Recommended article: Q4493202
Recommended article: Q4311747
description: scientific article; zbMATH DE number 1053443