On the Stability of Quadratic Functional Equations

Jung Rye Lee; Jong Su An; Choonkil Park
January 2008
Abstract & Applied Analysis;2008, p1
Academic Journal
Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx - y) = 2k²f (x) + 2f (y) for all x, y ϵ X if and only if the mapping f : X → Y satisfies f (x + y) + f(x - y) = 2f(x) + 2f(y) for all x, y ϵX. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.


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