On two-variable means with variable weights
type: Item
instance of: scholarly article
title: On two-variable means with variable weights
zbMATH Open document ID: 1087.39024
author: Gyula Maksa
author: Zoltán Daróczy
author: Zsolt Páles
published in: Aequationes Mathematicae
publication date: 2004-11-26T00:00:00Z
review text: The two-variable equality problem of two weighted quasi-arithmetic means was solved by \textit{L. Losonczi} [Aequationes Math. 58, 223--241 (1999; Zbl 0939.39015)] under the supposition of six times differentiability of the functions involved. The authors first prove a regularity theorem saying that every solution of a Pexider type functional equation with two unknown functions -- one strictly monotonic and continuous, the other positive (only) -- is infinitely many times differentiable. Therefore, Losonczi's result can be applied, yielding six families of solutions of the problem in the just described class of functions.
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 2119232
zbMATH Keywords: weighted quasi-arithmetic mean
zbMATH Keywords: Pexider type functional equation
zbMATH Keywords: regularity theorem
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
full work available at URL: s00010-003-2693-7
OpenAlex ID: W2062839537
DOI: 10.1007/S00010-003-2693-7
description: scientific article; zbMATH DE number 2119232