Quartic functional equations
type: Item
instance of: scholarly article
title: Quartic functional equations
zbMATH Open document ID: 1072.39024
author: Sang H. Lee
author: Sung Mo Im
author: In Sung Hwang
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-23T00:00:00Z
review text: In analogy to the ``quadratic functional equation'' \[ f(x+y)+f(x-y)=2f(x)+2f(y), \] that is, \(_s\Delta^2_y f(x)=2f(y),\) the authors call \[ f(2x+y)-4f(x+y)+6f(y)-4f(x-y)+f(2x-y)=4! f(x) \] (rather than \(_s\Delta^4_y f(x):= f(x+2y)-4f(x+y)+6f(x)-4f(x-y)+f(x-2y)=4! f(y)\)) ``quartic functional equation''. They offer its general solution from the real vector space into a real vector space (using solutions of the quadratic equation and four pages of calculations including up to 18-line equations) and a stability theorem for functions from a real normed linear space into a real Banach space.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 2182070
zbMATH Keywords: stability
zbMATH Keywords: real vector spaces
zbMATH Keywords: real normed linear spaces
zbMATH Keywords: real Banach spaces
zbMATH Keywords: quadratic functional equation
zbMATH Keywords: quartic functional equation
zbMATH Keywords: general solution
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.12.062
OpenAlex ID: W2066223768
cites work: Q3992445
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DOI: 10.1016/J.JMAA.2004.12.062
description: scientific article; zbMATH DE number 2182070