On the quadratic functional equation modulo a subgroup
type: Item
instance of: scholarly article
title: On the quadratic functional equation modulo a subgroup
zbMATH Open document ID: 1094.39021
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2006-04-04T00:00:00Z
review text: Let \(X\) be a topological vector space, \(Y\) a topological abelian group and \(K\) a discrete subgroup of \(Y\). The author considers mappings \(f:X\to Y\) continuous at the origin and satisfying the quadratic equation modulo \(K\): \[ f(x+y)+f(x-y)-2f(x)-2f(y)\in K,\qquad x,y\in X. \] He proves that for each such a mapping \(f\) there exists a quadratic function \(Q:X\to Y\) continuous at the origin an such that \[ f(x)-f(0)-Q(x)\in K,\qquad x\in X. \] Also the ``pexiderized'' congruence: \[ f_1(x+y)+f_2(x-y)-f_3(x)-f_4(y)\in K,\qquad x,y\in X \] and its particular form: \[ f(x+y)+f(x-y)-g(x)-g(y)\in K,\qquad x,y\in X \] are investigated.
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5017249
zbMATH Keywords: quadratic functional equation
zbMATH Keywords: functional congruence
zbMATH Keywords: topological vector space
zbMATH Keywords: topological abelian group
zbMATH Keywords: pexiderized congruence
author: Soon-Mo Jung
reviewed by: Jacek Chmieliński
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5017249