Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces
نویسندگان
چکیده
منابع مشابه
Stability of cubic and quartic functional equations in non-Archimedean spaces
We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2(k − k)f(x) for all k ∈ N and the quartic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2k(k − 1)f(x)− 2(k − 1)f(y) for all k ∈ N in non-Archimedean normed spaces.
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A classical question in the theory of functional equations is the following: “When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E?” If the problem accepts a solution, we say that the equation E is stable. The first stability problem concerning group homomorphisms was raised by Ulam [30] in 1940. We are given a group G and...
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ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2009
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-009-9512-7