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

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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Veröffentlicht in:Abstract and applied analysis 2009, Vol.2009 (2009), p.1-11
Hauptverfasser: Gordji, Madjid Eshaghi, Khodaei, H.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1085-3375
1687-0409