On two functional equations related to a result of Grégoire de Saint-Vincent
type: Item
instance of: scholarly article
title: On two functional equations related to a result of Grégoire de Saint-Vincent
zbMATH Open document ID: 0836.39005
DOI: 10.1007/BF03322237
author: Claudi Alsina
author: J.-L. García Roig
published in: Results in Mathematics
publication date: 1995-09-04T00:00:00Z
review text: Let \(f\) be a continuous function from \((- \infty, + \infty)\) into \((0, + \infty)\). The following conditions are equivalent: \[ f \left( {x + 2y \over 3} \right) f \left( {2x + y \over 3} \right) = f(x) f(y) \] for all \(x,y\) in \(\mathbb{R}\), \[ f(x)f \left( {x + 2y \over 3} \right) + f \left( {2x + y \over 3} \right) f(y) = f \left( {x + 2y \over 3} \right)^2 + f \left( {2x + y \over 3} \right)^2 \] for all \(x,y\) in \(\mathbb{R}\), and \[ f(x) = Ae^{Bx} \] for some positive constants \(A,B\) and for all \(x \in \mathbb{R}\). An open problem is posed.
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 792568
zbMATH Keywords: cube duplication
zbMATH Keywords: functional equations
reviewed by: Andrzej Smajdor
MaRDI profile type: Publication
cites work: Q5514010
cites work: Q4156723
description: scientific article; zbMATH DE number 792568