On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations
type: Item
instance of: scholarly article
title: On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations
zbMATH Open document ID: 1167.39014
DOI: 10.1155/2009/923476
published in: Abstract and Applied Analysis
publication date: 2009-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/55826
review text: Summary: We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations \[ \begin{multlined} f(ax+by)+f(ax - by)\\ =(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x - y)+(2a^{2} - ab - b^{2})f(x)+(b^{2} - ab)f(y)\end{multlined} \] where \(a, b\) are nonzero fixed integers with \(b\neq \pm a, - 3a\), and \[ f(ax+by)+f(ax - by)=2a^{2}f(x)+2b^{2}f(y) \] for fixed integers \(a, b\) with \(a,b\neq 0\) and \(a\pm b\neq 0\).
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5574392
zbMATH Keywords: Hyers-Ulam-Rassias stability
zbMATH Keywords: Ulam-Gavruta-Rassias stabilities
zbMATH Keywords: quadratic functional equations
Wikidata QID: Q58646696
author: Madjid Eshaghi Gordji
author: H. Khodaei
MaRDI profile type: Publication
OpenAlex ID: W2083552781
cites work: Q5511350
cites work: On the Stability of the Linear Functional Equation
cites work: On the stability of the linear transformation in Banach spaces
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: Q3374520
cites work: On approximation of approximately linear mappings by linear mappings
cites work: Q3733629
cites work: Q3721188
cites work: Solution of a problem of Ulam
cites work: Q4202311
cites work: On stability of additive mappings
cites work: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
cites work: Q5460093
cites work: Extended Hyers–Ulam stability for Cauchy–Jensen mappings†
cites work: Q5458104
cites work: Solution of a quadratic stability Hyers-Ulam type problem
cites work: Q4873598
cites work: Q4697104
cites work: Refined Hyers--Ulam approximation of approximately Jensen type mappings
cites work: Q3024474
cites work: Q3992445
cites work: Quadratic functional equation and inner product spaces
cites work: Proprieta’ locali e approssimazione di operatori
cites work: Remarks on the stability of functional equations
cites work: On the stability of the quadratic mapping in normed spaces
cites work: Q4913374
cites work: On the stability of quadratic functional equations
description: scientific article; zbMATH DE number 5574392