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

Gordji, M. Eshaghi; Khodaei, H.
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
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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