On Jensen's functional equation
type: Item
instance of: scholarly article
title: On Jensen's functional equation
zbMATH Open document ID: 0755.39008
DOI: 10.1007/BF01835703
author: J. C. Parnami
author: Harkrishan L. Vasudeva
published in: Aequationes Mathematicae
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/137464
review text: The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2\mid\;x\in G\}\). While this is not true in general for nonabelian groups, a partial result (in the ``only if'' direction) is presented in this case too.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 92522
zbMATH Keywords: Jensen's functional equation
zbMATH Keywords: 2-cancellativity
zbMATH Keywords: Zorn's lemma
zbMATH Keywords: abelian groups
zbMATH Keywords: homomorphisms
MaRDI profile type: Publication
cites work: Q5514010
cites work: Q3808594
cites work: A generalization of the cosine-sine functional equation on groups
cites work: Q3854084
cites work: Q3218572
cites work: Jensen's functional equation on groups
description: scientific article; zbMATH DE number 92522