منابع مشابه
Approximate multi-additive mappings in 2-Banach spaces
A mapping $f:V^n longrightarrow W$, where $V$ is a commutative semigroup, $W$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings i...
متن کاملApproximate Quartic and Quadratic Mappings in Quasi-Banach Spaces
The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms. Let G1, · be a group, and let G2, ∗ be a metric group with the metric d ·, · . Given > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h x · y , h x ∗ h y < δ for all x, y ∈ G1, then there exists a homomorphism H :...
متن کاملApproximate additive and quadratic mappings in 2-Banach spaces and related topics
Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthes...
متن کاملapproximate multi-additive mappings in 2-banach spaces
a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...
متن کاملApproximate a quadratic mapping in multi-Banach spaces, a fixed point approach
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06886-7