Refinements and extensions of an inequality. III
type: Item
instance of: scholarly article
title: Refinements and extensions of an inequality. III
zbMATH Open document ID: 0932.26011
author: K. Appert
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-05-31T00:00:00Z
review text: The authors give a complete characterization of the set \((x,y)\subset (-\infty,\infty)\times(-\infty,\infty)\) such that \[ (b^{x+ y}-a^{x+y})/(b^x- a^x)\geq {x+ y\over x} \Biggl({a+ b\over 2}\Biggr)^y, \] where \(a,b>0\) are given real numbers. In the proof the theory of extended mean values \(E(r,s; x,y)\) introduced by \textit{E. B. Leach} and \textit{M. C. Sholander} [J. Math. Anal. Appl. 92, 207-223 (1983; Zbl 0517.26007)] is applied. This method proves the importance of general means and their inequalities. [For Part II see J. Math. Anal. Appl. 211, No. 2, 616-620 (1997; preceding review].
reviewed by: József Sándor
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 1267985
zbMATH Keywords: convexity
zbMATH Keywords: completely monotonic functions
zbMATH Keywords: inequalities for means
zbMATH Keywords: extended mean values
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6104
OpenAlex ID: W2009843680
cites work: Extended Mean Values
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DOI: 10.1006/JMAA.1998.6104
description: scientific article; zbMATH DE number 1267985