On solutions of the Fréchet functional equation
type: Item
instance of: scholarly article
title: On solutions of the Fréchet functional equation
zbMATH Open document ID: 1118.39008
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-06-06T00:00:00Z
review text: The paper begins with a survey on the Fréchet equation \(\Delta_h^n f=0,\) where \(f: \mathbb{R}\to\mathbb{R}\), \((\Delta_h^1 f)(x)=f(x+h)-f(x),\) \(\Delta_h^{n+1} =\Delta_h^1(\Delta_h^n),\) \( x\in\mathbb{R},\) \(h\in]0,\infty[,\) \(n\in \mathbb{N},\) its particular cases the Cauchy and Jensen equations, its generalizations where there are \(h_1,h_2,\dots\) in place of just one \(h\) or \(x_1,x_2,\dots\) in place of \(x.\) Then the authors offer new proofs of results on these equations and results on the graphs of their solutions.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5161762
zbMATH Keywords: difference operators
zbMATH Keywords: Darboux theorem
zbMATH Keywords: Cauchy functional equation
zbMATH Keywords: Jensen functional equation
zbMATH Keywords: Fréchet functional equation
author: Jose Maria Almira
author: Antonio Jesús López-Moreno
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.11.002
OpenAlex ID: W2004207633
cites work: Q4707122
cites work: Q3069645
cites work: Q2968969
cites work: Some properties of convex functions of higher orders
cites work: On some properties of polynomial functions
cites work: On extension of polynomial functions
cites work: Q4305783
cites work: On vanishing n-th ordered differences and Hamel bases
cites work: Q3255661
cites work: Q4520097
cites work: Q3480744
cites work: Fréchet's equation and Hyers theorem on noncommutative semigroups
DOI: 10.1016/J.JMAA.2006.11.002
description: scientific article; zbMATH DE number 5161762