Note on a functional equation related to the power means
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.39015
author: Justyna Sikorska
publication date: 2001-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/226043
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1604180
zbMATH Keywords: weighted quasi-arithmetic mean
zbMATH Keywords: additive function
zbMATH Keywords: exponential function
MaRDI profile type: Publication
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title: Note on a functional equation related to the power means
published in: Mathematica Pannonica
review text: Solutions of the functional equation \( x + g(y + f(x)) = y + g(x + f(y)) \) are determined under the assumption that (at least) one of the unknown functions is additive or has the form of a weighted quasi-arithmetic mean with an exponential generator. Continuity assumptions are required when \(f\) is supposed to belong to a given class.
reviewed by: Zoltán Boros
description: scientific article; zbMATH DE number 1604180