On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a...

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Main Authors: M. Eshaghi Gordji, H. Khodaei
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/923476
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author M. Eshaghi Gordji
H. Khodaei
author_facet M. Eshaghi Gordji
H. Khodaei
author_sort M. Eshaghi Gordji
collection DOAJ
description We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0.
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spelling doaj-art-2fbdc4296fee4ac9a4ec27d06adb71b72025-08-20T02:08:11ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/923476923476On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional EquationsM. Eshaghi Gordji0H. Khodaei1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranWe achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0.http://dx.doi.org/10.1155/2009/923476
spellingShingle M. Eshaghi Gordji
H. Khodaei
On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
Abstract and Applied Analysis
title On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
title_full On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
title_fullStr On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
title_full_unstemmed On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
title_short On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
title_sort on the generalized hyers ulam rassias stability of quadratic functional equations
url http://dx.doi.org/10.1155/2009/923476
work_keys_str_mv AT meshaghigordji onthegeneralizedhyersulamrassiasstabilityofquadraticfunctionalequations
AT hkhodaei onthegeneralizedhyersulamrassiasstabilityofquadraticfunctionalequations