A one-parameter family of bivariate means
type: Item
instance of: scholarly article
title: A one-parameter family of bivariate means
zbMATH Open document ID: 1281.26026
author: Edward Neuman
published in: Journal of Mathematical Inequalities
publication date: 2013-10-24T00:00:00Z
full work available at URL: jmi-07-35.pdf
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 6219468
zbMATH Keywords: bivariate means
zbMATH Keywords: Seiffert means
zbMATH Keywords: Neuman-Sándor means
zbMATH Keywords: logarithmic means
zbMATH Keywords: Schwab-Borchardt means
zbMATH Keywords: inequalities convex combinations
MaRDI profile type: Publication
OpenAlex ID: W2326283611
DOI: 10.7153/JMI-07-35
review text: It would seem unlikely that anything very new could be said about symmetric two variable means and yet here is a paper that does just that. It is well written and very lucid. Given such a mean \(N\) and a number \(p\), \(-1\leq p\leq 1,\) define \(N_p(x,y) = N\bigl({1+p\over 2}x+{1-p\over 2}y, {1-p\over 2}x+{1+p\over 2}y\bigr)\). The order relations between various standard means are well known; the same order is maintained in the new class of means when the standard means are used as \(N.\) The new class of means is studied and most if not all the important properties obtained in a very simple manner.
reviewed by: P. S. Bullen
description: scientific article; zbMATH DE number 6219468